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This handy Math in Focus Grade 6 Workbook Answer Key Chapter 13 Lesson 13.1 Collecting and Tabulating Data detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 13 Lesson 13.1 Answer Key Collecting and Tabulating Data

Math in Focus Grade 6 Chapter 13 Lesson 13.1 Guided Practice Answer Key

Complete. Use the data in the table.

Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.

Then she used a tally chart to record what she had found.

Question 1.
Copy and complete the table by counting the tally marks.

Answer:

Explanation:
Give that,
Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.
We know that the tally marks are a way to mark or record your counting.
Tally marks are a numerical system used to make counting easier.
As the name suggests, it is a system that helps keep the “tally” of things by number.
Tally marks are commonly used for counting scores, points, number of people, etc.
Tally marks differ from country to country, as each culture has developed its own systems.

Question 2.
More of Emma’s classmates have brother or sister than any other number.
Answer:
1

Explanation:
Given that, Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.
with reference to the above Tally marks and frequency table,
Emma’s classmates have 1 brother or sister than any other number.

Question 3.
of Emma’s classmates have 3 brothers or sisters in their families.
Answer:
5 of Emma’s classmates have 3 brothers or sisters in their families.

Explanation:
Given that, Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.
with reference to the above Tally marks and frequency table,
5 of Emma’s classmates have 3 brothers or sisters in their families.

Question 4.
of Emma’s classmates have 4 brothers or sisters in their families.
Answer:
2 of Emma’s classmates have 4 brothers or sisters in their families.

Explanation:
Given that, Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.

with reference to the above Tally marks and frequency table,
2 of Emma’s classmates have 4 brothers or sisters in their families.

Question 5.
How many more of Emma’s classmates have 2 brothers or sisters than 5 or more brothers or sisters in their families?
Answer:
6 of Emma’s classmates have 2 brothers or sisters than 5 or more brothers or sisters in their families.

Explanation:
Given that, Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.
7 of Emma’s classmates have 2 brothers or sisters in their families
1 of Emma’s classmates have more then 5 brothers or sisters in their families
if we subtract as follows
7 – 1 = 6
6 many more of Emma’s classmates have 2 brothers or sisters than 5 or more brothers or sisters in their families.

Question 6.
Emma has classmates altogether.
Answer:
27

Explanation:
Given that, Emma used a questionnaire to find out the number of brothers or sisters her classmates have in their families.
Then she used a tally chart to record what she had found.

So, Emma has 27 classmates altogether.

Hands-On Activity

COLLECT, TABULATE, AND INTERPRET DATA

Materials:

• blank table
• ruler
• collection of pencils

Work in groups of three or four.

Step 1: Collect a set of pencils of various lengths. Use a ruler to measure the length of each pencil to the nearest centimeter. Use tally marks to record the data.
Step 2: Tally your results on a table like the one below. Then count the tally marks to complete the table.

Step 3: Write at least four questions about the data in the table using these phrases.

Answer:

Explanation:
We know that the tally marks are a way to mark or record your counting.
Tally marks are a numerical system used to make counting easier.
As the name suggests, it is a system that helps keep the “tally” of things by number.
Tally marks are commonly used for counting scores, points, number of people, etc.
Tally marks differ from country to country, as each culture has developed its own systems.

Write at least four questions about the data in the above table.

1) How many pencils are of shortest lengths?
Answer:
5 pencils.

Explanation:
Given that to collect a set of pencils of various lengths.
Use a ruler to measure the length of each pencil to the nearest centimeter.
Use tally marks to record the data.
Tally your results on a table like the one above.
Then count the tally marks to complete the table.
with reference to the above table, there are 5 pencils of length 14 cm are shortest.

2) How many pencils are of longest lengths?
Answer:
2 pencils.

Explanation:
Given that to collect a set of pencils of various lengths.
Use a ruler to measure the length of each pencil to the nearest centimeter.
Use tally marks to record the data.
Tally your results on a table like the one above.
Then count the tally marks to complete the table.
with reference to the above table, there are 2 pencils are of length 18 cm are longest.

3) How many pencils are of more number of which lengths?
Answer:
10 pencils.
Explanation:
Given that to collect a set of pencils of various lengths.
Use a ruler to measure the length of each pencil to the nearest centimeter.
Use tally marks to record the data.
Tally your results on a table like the one above.
Then count the tally marks to complete the table.
with reference to the above table, there are 10 pencils are of length 16 cm long.

4) Altogether total how many pencils are of different lengths?
Answer:
28 pencils.

Explanation:
Given that to collect a set of pencils of various lengths.
Use a ruler to measure the length of each pencil to the nearest centimeter.
Use tally marks to record the data.
Tally your results on a table like the one above.
Then count the tally marks to complete the table.
with reference to the above table, there are 28 pencils are of different lengths.

Math in Focus Course 1B Practice 13.1 Answer Key

Copy and complete the table. Solve.

Question 1.
A shampoo company wanted to find out more about its customers. So they asked 30 customers to indicate their income bracket:
Below $500 per week
$500—$1,000 per week
Over $1,000 per week
A tally chart was used to record the findings.

How many customers have a weekly income of $1,000 or less?
Answer:
26 customers.

Explanation:
Given that, A shampoo company wanted to find out more about its customers.
So they asked 30 customers to indicate their income bracket:
Below $500 per week
$500—$1,000 per week
Over $1,000 per week
A tally chart was used to record the findings.
with reference to the table below,
the total number of customers have a weekly income of $1,000 or less are 26.
customers have a weekly income of $500 – $1,000 is 19 and
customers have a weekly income of $500 are 7
19 + 7 = 26 customers

Question 2.
Fifty students were asked their level of satisfaction with the school’s music program. The following responses were the choices provided:
(a) very satisfied (b) satisfied (c) neutral (d) dissatisfied (e) very dissatisfied.

a) How many students are satisfied or very satisfied?
Answer:
students are satisfied = 7
students are very satisfied = 2

Explanation:
Given that, Fifty students were asked their level of satisfaction with the school’s music program.
The following responses were the choices provided:
(a) very satisfied (b) satisfied (c) neutral (d) dissatisfied (e) very dissatisfied.

With reference to the above table, students are satisfied or very satisfied is shown below.
students are satisfied = 7
students are very satisfied = 2

b) Based on the results of the survey, should the school think about changing the program? Explain your reasoning.
Answer:
YES

Explanation:
Given that, Fifty students were asked their level of satisfaction with the school’s music program.
The following responses were the choices provided:
(a) very satisfied (b) satisfied (c) neutral (d) dissatisfied (e) very dissatisfied.
Based on the above table results of the survey,
the school think about changing the program due to less satisfied and very satisfied out of 50 students.

Question 3.
A mathematics teacher wanted to find out how many hours per week his students spent on math homework. The average number of hours reported by each student is shown.
5, 3, 6, 8, 2, 4, 2, 1, 9, 1, 9, 6, 4, 6, 5, 1, 10, 1, 5, 6, 7, 8, 6, 10, 7, 5, 2, 8
Arrange the numbers in ascending order.
1,1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10

How many students spent more than 3 hours per week on their math homework?
Answer:
20 students spent more than 3 hours and less then per week on their math homework.

Explanation:
Given that, A mathematics teacher wanted to find out how many hours per week his students spent on math homework.
The average number of hours reported by each student is shown.
5, 3, 6, 8, 2, 4, 2, 1, 9, 1, 9, 6, 4, 6, 5, 1, 10, 1, 5, 6, 7, 8, 6, 10, 7, 5, 2, 8
Arrange the numbers in ascending order.
1,1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10
With reference to the given information,
13 students spent more than 4 hours per week on their math homework.
13 + 7 = 20

Question 4.
Shelly conducted a survey among her friends. She asked them to choose their favorite fruit from this list of fruits: apple, orange, strawberry, grapes, and peach. These are the data she collected:

Tabulate the data.

What is the favorite fruit of Shelly’s friends?
Answer:
Strawberry.

Explanation:
Given that, Shelly conducted a survey among her friends.
She asked them to choose their favorite fruit from this list of fruits: apple, orange, strawberry, grapes, and peach.
These are the data she collected:
With reference to the survey among her friends.
Shelly friend’s favorite fruit from the list of fruits: apple, orange, strawberry, grapes, and peach:
Strawberry is favorite fruit as shown below.

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 13 Introduction to Statistics detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 13 Answer Key Introduction to Statistics

Math in Focus Grade 6 Chapter 13 Quick Check Answer Key

Complete. Use the data in the line plot.

The line plot shows the weight, in pounds, of cartons of apples in a store. Each x represents 1 carton of apples.

Question 1.
What is the weight of the lightest carton of apples?
Answer:
45 lb
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.
Each x represents 1 carton of apples.

So, the weight of one apple carton box (x) = 45 lb
= 45 lb

Question 2.
What is the weight of the heaviest carton of apples?
Answer:
378 lb
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.
Each x represents 1 carton of apples.

9 apple carton box X 45 lb.
The weight of the heaviest carton of apples is = 378 lb

Question 3.
What is the difference in weight between the heaviest carton of apples and the lightest carton of apples?
Answer:
333 lb
Explanation:
We know from the above questions that the weight of the heaviest carton of apples = 378 lb
The weight of the lightest carton of apples = 45 lb
The difference in weight between the heaviest carton of apples and the lightest carton of apples,
378 – 45 = 333 lb

Question 4.
How many cartons weigh more than 41 pounds?
Answer:
15 cartons weigh more than 41 pounds.
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.

9 cartons weigh 42 pounds
3 cartons weigh 43 pounds
2 cartons weigh  44 pounds
1 cartons weigh  45 pounds
9 + 3 + 2 + 1 =  15
15 cartons weigh more than 41 pounds.

Question 5.
How many cartons weigh less than 40 pounds?
Answer:
7 cartons weighs less than 40 pounds.
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.

5 cartons weigh  38 pounds.
2 cartons weigh  39 pounds.
5 + 2 =  7
So, 7 cartons weigh less than 40 pounds.

Question 6.
How many cartons weigh 44 pounds each?
Answer:
2 cartons weighs 44 pounds each.
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.
So, 2 cartons weighs 44 pounds each.

Question 7.
How many cartons are there in all?
Answer:
32 cartons are there in all.
Explanation:
The line plot shows the weight, in pounds, of cartons of apples in a store.

So, 32 cartons are there in all.

Question 8.
How many times as many cartons of apples weigh 40 pounds as the number of cartons of apples that weigh 43 pounds?
Answer:
2 times.
Explanation:
cartons of apples weigh 40 pounds is 6 cartons.
cartons of apples that weigh 43 pounds is 3 cartons.
Number of times as many cartons of apples weigh 40 pounds as the number of cartons of apples that weigh 43 pounds = 6/3 = 2 times.

Question 9.
The ratio of the number of cartons of apples that weigh 42 pounds to the ‘ number of cartons of apples that weigh 40 pounds is .
Answer:
3 : 2
Explanation:
cartons of apples weigh 42 pounds is 9 cartons.
cartons of apples that weigh 40 pounds is 6 cartons.
Ratio of both the cartons = 9 : 6
By simplifying we get 3 : 2
So, the ratio of the number of cartons of apples that weigh 42 pounds to the ‘ number of cartons of apples that weigh 40 pounds is 3 : 2

Question 10.
The number of cartons of apples that weigh 41 pounds is % of the total number of cartons of apples.
Answer:
12.5
Explanation:
The number of cartons of apples that weigh 41 pounds is 4 cartons.
The total number of cartons of apples = 32
4/32 = 0.125
So, the number of cartons of apples that weigh 41 pounds is 12.5 % of the total number of cartons of apples.

This handy Math in Focus Grade 6 Workbook Answer Key Cumulative Review Chapters 12-14 detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Cumulative Review Chapters 12-14 Answer Key

Concepts and Skills

Match each of the solid figures to its net. (Lesson 12.1)

Question 1.

Answer:
1 – b
2 – a
3 – c

Explanation:
A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

A pyramid is a three-dimensional figure. It has a flat polygon base.
All the other faces are triangles and are called lateral faces.
The number of lateral faces equals the number of sides on its base.
Its edges are the line segments formed by two intersecting faces.

Find the surface area and volume of each prism. (Lesson 12.1, 12.2)

Question 4.

Answer:
Surface Area SA = 1308 square meter.
Volume V = 2808 cubic meters.

Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
SA=2lw+2lh+2hw
SA = 2x 26×9 + 2x 26×12 + 2x 9x 12
SA = 468 + 624 + 216
SA = 1308 sq meter
Volume of a cuboid:
The volume of cuboid is the quantity that is used to measure the space in a cuboid.
A cuboid is a three-dimensional shape that can be seen around us very often.
The term volume is used in measuring the capacity of any shape based on its dimensions such as: length, breadth, and, height. To calculate the volume of a cuboid,
V = l × b × h = lbh
V = 26 x 9 x 12
V = 2808 cubic meters.

Question 5.

Answer:
Surface Area = 828 square inches.
Volume = 1080 cube inches.

Explanation:
The surface area of triangular prism is the total area of all its faces.
A triangular prism is a prism that has two congruent triangular faces and three rectangular faces that join the triangular faces.
has 6 vertices, 9 edges, and 5 faces. Let us learn more about the surface area of a triangular prism.

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S₁ +S₂ + S₃)L + bh
=(12 + 15 + 9)20 + 15 x 20
= 720 + 108
= 828 square inches.
Volume:
V =(1/2)( l × b × h) = (0.5)lbh
V = 0.5 x 20 x 9 x 12
V = 1,080 cubic meters.

Solve. Show your work. (Lessons 14.1, 14.2)

Question 6.
The data set shows the lengths (in inches) of seven pieces of wire.
7.9, 6.8, 7.6, 9.9, 10.1,9.1, 10.9
Find the mean and median lengths of these seven pieces of wire.
Answer:
mean = 8.9
median = 9.1

Explanation:
Given set of data, 7.9, 6.8, 7.6, 9.9, 10.1,9.1, 10.9
arrange the given data in the ascending order,
6.8, 7.6, 7.9, 9.1, 9.9, 10.1, 10.9
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{6.8 + 7.6 + 7.9 + 9.1 + 9.9 + 10.1 + 10.9}{7}\)
mean = \(\frac{62.9}{7}\)
mean = 8.9
Median:
median : Middle value is the median of a given data set.
6.8, 7.6, 7.9, 9.1, 9.9, 10.1, 10.9
the above data has 7 observations,
So, 9.1 in the middle of the order sequence is the median.
median = 9.1

Question 7.
The data set shows the weights (in pounds) of 9 vases.
8.8, 8.3, 7.7, 11.6, 9.9, 8.9, 10.4, 9.6, 8.5
Find the mean and median weights of these 9 vases.
Answer:
Mean = 9.3lb
Median = 8.9lb

Explanation:
Given set of data, 8.8, 8.3, 7.7, 11.6, 9.9, 8.9, 10.4, 9.6, 8.5
arrange the given data in the ascending order,
7.7, 8.3, 8.5, 8.8, 8.9, 9.6, 9.9, 10.4, 11.6
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{7.7 + 8.3 + 8.5 + 8.8 + 8.9 + 9.6 + 9.9 + 10.4 + 11.6}{9}\)
mean = \(\frac{83.7}{9}\)
mean = 9.3

Median:
median : Middle value is the median of a given data set.
7.7, 8.3, 8.5, 8.8, 8.9, 9.6, 9.9, 10.4, 11.6
the above data has 9 observations,
8.9 in the middle of the order sequence is the median.

Question 8.
The data set shows the heights (in feet) of 8 trees.
53, 56, 65, 61, 67, 60, 52, 48
Find the mean and median heights of these 8 trees.
Answer:
Mean = 57.75
Median = 58

Explanation:
Given set of data, 53, 56, 65, 61, 67, 60, 52, 48
arrange the given data in the ascending order,
48, 52, 53, 56, 60, 61, 65, 67
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{48 + 52 + 53 + 56 + 60 + 61 + 65 + 67}{8}\)
mean = \(\frac{462}{8}\)
mean = 57.75

Median:
median : Middle value is the median of a given data set.
48, 52, 53, 56, 60, 61, 65, 67
the above data has 8 observations,
So, 56, 60 are in the middle of the order sequence is the median.
the average of (56 + 60)/2 = 116/2 = 58

The volume of each triangular prism is 497 cubic feet. Find the height of the triangular base. Round your answers to the nearest tenth of a foot. (Lesson 12.3)

Question 9.

Answer:
6.9 feet.

Explanation:
Volume:
V =(1/2)( l × b × h) = (0.5) lbh
V = 0.5 x 18 x 8 x h
497 = 72h
h = \(\frac{497}{72}\)
h = 6.9 ft

Question 10.

Answer:
9.94 ft

Explanation:
Volume:
V =(1/2)( l × b × h) = (0.5) lbh
V = 0.5 x 20 x 5 x h
497 = 50h
h = \(\frac{497}{50}\)
h = 9.94 ft

Solve. (Lesson 12.3)

Question 11.
The solid below is made of identical cubes. The volume of the solid is 405 cubic centimeters. Find the edge length of each cube.

Answer:
3 cm

Explanation:
The volume of a cube is length x width x height.
Since it’s a cube, though, the length, width, and height are all equal, and equivalent to the length of one edge of the cube.
Therefore, to find the length of an edge of the cube,
just find the cube root of the volume.
Formula for volume of cube is given by V=a³
where a is edge of the cube.
Given,
volume = 405 cm³
The volume of the solid is 405 cubic centimeters, there are 15 cubes
405 /15 = 27
volume = 27 cm³
a³  = 27
a = 3 cm

Draw a dot plot and a histogram for the set of data. Include a title. (Lessons 13.2, 13.3)

Question 12.
The number of pieces of fruits eaten in the past two days by each of 30 students was recorded below.

a) Represent the set of data with a dot plot.
Answer:

Explanation:
Each dot represent one children,
the number of pieces of fruits eaten in the past two days by each of 30 students was recorded with orange dots.

b) Group the data into suitable intervals and tabulate them.
Answer:

Explanation:
With an interval of one numbers all dots are tabulated in a table as shown in the above table for the above data given.

c) Draw a histogram using the intervals from part b). Briefly describe the data.
Answer:

Explanation:
Histogram drawn using the intervals from the data in the table as shown in the above table.
x-axis shows the number of students and y-axis shows number of pieces of fruits.
With an interval of one number as shown above.
The shape of the histogram is right skewed.

Describe the data. (Lesson 13.3)

Question 13.
The histogram shows the number of floors each building has in a particular city. Briefly describe the data.

Answer:
Total buildings = 84
Most of the buildings have 21 to 40 floors.
The range of the data is 119.
Most of the data values are to the right of the interval 21-40,
The shape of the histogram is right skewed.

Explanation:

The above histogram shows the number of floors each building has in a particular city.
As, total buildings, range of the data, intervals of the data and shape of the histogram are described.

Problem Solving

Draw a dot plot for each set of data. Use your dot plot to answer each question. (Chapters 13, 14)

Question 14.
The data set shows the number of text messages sent by Emily in 14 days.

a) Represent the set of data with a dot plot.
Answer:

Explanation:
The above dot plot shows the data set and the number of text messages sent by Emily in 14 days.. Each dot represents one message.

b) Find the mean, median, and mode of the data set.
Answer:
Mean = 3
Mode = 7
Median = 4

Explanation:
The above dot plot shows the data set and the number of text messages sent by Emily in 14 days.. Each dot represents one message.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x2 + 1×2 + 2×1 + 3×2 + 5×2 + 7×4 + 8×1 }{14}\)
mean = \(\frac{0 + 2 + 2 + 6 + 10 + 14 + 8 }{14}\)
mean = \(\frac{42}{14}\)
mean = 3

Mode:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
0, 0, 1, 1, 2, 3, 3, 5, 5, 7, 7, 7, 7, 8
the above data has 14 observations,
So,  7 appears most frequently, is the mode of a given data.

Median:
median : Middle value is the median of a given data set.
0, 0, 1, 1, 2, 3, 3, 5, 5, 7, 7, 7, 7, 8
the above data has 14 observations,
Median is the average value of the 3 & 5
(3 + 5 )/2 = 8/2 = 4
So, 4 in the middle of the order sequence is the median.

Question 15.
The data set shows the number of salads served in a cafe for each of 20 days.

a) Represent the set of data with a dot plot.
Answer:

Explanation:
The given data set shows the number of salads served in a Cafe for each of 20 days.
Each dot represents the number of salad served in Cafe.

b) Find the mean, median, and mode of the data set.
Answer:
Mean = 21.8
Median = 22
Mode = 24

Explanation:
The given data set shows the number of salads served in a Cafe for each of 20 days.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{1×16 + 1×17 + 1×18 + 2×19 + 2×20 + 2×21 + 3×22 + 2×23 + 4x 24+ 2×26 }{14}\)
mean = \(\frac{16 + 17 + 18+ 38 + 40 + 42 + 66 + 46 + 96 + 52 }{14}\)
mean = \(\frac{431}{20}\)
mean = 22

Mode:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
16, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 24, 26, 26
the above data has 20 observations,
So,  24 appears most frequently, is the mode of a given data.

Median:
median : Middle value is the median of a given data set.
16, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 24, 26, 26
the above data has 14 observations,
Median is the average value of the 3 & 5
(22 + 22 )/2 = 44/2 = 22
So, 22 in the middle of the order sequence is the median.

Solve. Show your work. (Chapter 12)

Question 16.
The square pyramid shown has congruent triangular faces. The area of one triangular face is 48 square inches. Find the surface area of the pyramid.

Answer:
112 Sq in

Explanation:
Surface Area = Base area + Lateral Area
Base area = Side X Side
BA = 8 x 8 = 64 Sq in
Lateral  Area LA = (1/2) Side x Height
LA = (1/2) x 8 x 12
LA = 48
Surface Area SA= Base area + Lateral Area
SA = 64 + 48  = 112 Sq in

Question 17.
The length of the aquarium shown is two times its width. The height of the aquarium is 18 inches. The aquarium is filled with water to a height of 16 inches. The volume of the water is 7,200 cubic inches.
a) Find the length of the base of the aquarium.
Answer:
Length = 30 inches.

Explanation:
The height of the aquarium is 18 inches.
The aquarium is filled with water to a height of 16 inches.
The volume of the water is 7,200 cubic inches.
Volume V =Length X Width X Height
V = l.w.h
Let x be the length of the width, and length of base if 2x
V =  2w x w x 16
7200 =32 . w²
225 = w²
w = 15
width w = 15 inches
Length of the base = 2xw
l = 2 x 15
l =30 inches.

b) Then find the amount of glass, in square inches, used to make the bottom and sides of the aquarium.

Answer:
Surface Area = 2070 square inches.

Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
SA=2lw+2lh+2hw
SA = 30×15 + 2x 18×15 + 2x 30×18
SA = 450 + 540 + 1080
SA = 2,070 sq inches.

Solve. (Chapter 13)

Question 18.
The table shows the number of hours each of 120 students spent helping their community in two months.

a) Find the value of x.
Answer:
x = 5

Explanation:
The given table shows the number of hours each of 120 students spent helping their community in two months.
x + 2x + 105 = 120
120 -105 = 3x
3x = 15
x = 5

b) Draw a histogram to represent the data. Briefly describe the data.
Answer:

Explanation:
The given table shows the number of hours each of 120 students spent helping their community in two months.
Histogram drawn using the intervals from the data in the table as shown in the above table.
Number of students is on x-axis and number of hours on y-axis.
Most of the data values are to the right of the interval 31-75,
The shape of the histogram is right skewed.

c) What percent of the students spent more than 55 hours helping their community?
Answer:
47.5 %

Explanation:
The given table shows the number of hours each of 120 students spent helping their community in two months.
The students spent more than 55 hours helping their community are,
18+16+13+10 = 57 hours
57 x 5 = 285 hours
Total 120 x 5 = 600 hours
The percent of the students spent more than 55 hours helping their community are,
57/120 = 0.475
0.475 x 100 = 47.5%

d) What percent of the students spent less than 46 hours helping their community?
Answer:
22.5%

Explanation:
The given table shows the number of hours each of 120 students spent helping their community in two months.
Number of the students spent less than 46 hours helping their community are,
5+9+13 = 27 hours.
27 x 5 = 135 hours.
Total 120 x 5 = 600 hours.
The percent of the students spent more than 55 hours helping their community are,
27/120 = 0.225
0.225 x 100 = 22.5%

Make a dot plot to show the data. Use your dot plot to answer each question. (Chapters 13, 14)

Question 19.
The table shows the results of a survey to find the number of television sets in 50 randomly chosen homes.

The total number of homes that have 0 or 1 television set is 15.

a) Find values of x and y. Then represent this set of data with a dot plot.
Answer:
x = 10
y = 4

Explanation:
The total number of homes that have 0 or 1 television set is 15.
y + 11 = 15
y = 4

total no of houses = 50
4 + 11 + 17 + x + 6 + 2 = 50
40 + x = 50
x = 10

b) Find the mean, median, and mode of the data set.
Answer:
Mean = 2.18
Median = 2
Mode = 2
Explanation:
mean = (0 x 4) + (1 x 11) + (2 x 17) + (3 x 10) + (4 x 6) + (5 x 2) ÷ 50
(11 + 34 + 30 + 24 + 10) ÷ 50
109 ÷ 50
Mean = 2.18

Median = no of houses ÷ 2 = 25
4 + 11 + 10 = 25
so the 25th home lies in the 17 homes which have 2 TV’s
Median = 2

Mode = 2
most of the houses have 2 TV’s

c) Briefly describe the data distribution and relate the measure of center to the shape of the dot plot.
Answer:
The given table shows the results of a survey to find the number of television sets in 50 randomly.
Histogram drawn using the intervals from the data in the table as shown in the above table.
Number of homes is on x-axis and number of televisions on y-axis.
Most of the data values are to the right of the interval only 1,
The shape of the histogram is right skewed.

d) A similar survey is carried out on another 30 randomly chosen homes and the mean number of television sets is found to be 1.9. If the two data sets are combined, find the mean number of television sets in the combined data set.
Answer:
Mean = 2.04

Explanation:
50 randomly chosen homes and the mean number of television sets is found to be 2.18.
30 randomly chosen homes and the mean number of television sets is found to be 1.9.
the mean number of television sets in the combined data set.
(2.18 + 1.9) ÷ 2
Mean = 2.04

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 14 Review Test detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 14 Review Test Answer Key

Concepts and Skills

Solve. Show your work.

Question 1.
The data set shows nine students’ scores in a science quiz. 9, 6, 6, 5, 9, 10, 1,4, 10
Find the mean and median score.
Answer:
mean = 6\(\frac{2}{3}\)
median = 6

Explanation:
To find the mean: The sum of the values by adding them all up.
9 + 6 + 6 + 5 + 9 + 10 + 1 + 4 +10 = 60
Divide the sum by the number of values in the data set.
60 ÷ 9
Simplify as = 20 ÷ 3 = 6\(\frac{2}{3}\)
To find the median: Arrange the data points from smallest to largest.
Given set of quiz scores are {9, 6, 6, 5, 9, 10, 1,4, 10}
Ascending order of the scores are {1, 4, 5, 6, 6, 9, 9, 10, 10}
If the number of data points is odd, the median is the middle data point in the list.
So, the median is 6.

Question 2.
The mean of a set of four numbers is 3.5. If a fifth number, x, is added to the data set, the mean becomes 4. Find the value of x.
Answer:
x = 6

Explanation:
Given that,
The mean of a set of four numbers is 3.5.
Total = 3.5 x 4 = 14
If a fifth number, x, is added to the data set, the mean becomes 4.
(14 + x) ÷ 5 = 4
14 + x = 20
x = 20 – 14
x = 6

Make a dot plot to show the data. Use your dot plot to answer the question.

Question 3.
The data set shows the number of vehicles at a highway intersection during morning rush hour on 15 working days.
12, 11, 4, 6, 9, 11, 4, 6, 12, 16, 11, 10, 8, 4, 5
Find the mean, median, and mode of the data set.
Answer:
mean = 8.6
median = 9
mode = 4 and 11

Explanation:
To find the mean:
The sum of the values by adding them all up.
12 + 11 + 4 + 6 + 9 + 11 + 4 + 6 + 12 + 16 + 11 + 10 + 8 + 4 + 5 = 129
Divide the sum by the number of values in the data set.
129 ÷ 15
To find the median:
Arrange the data points from smallest to largest.
Given set of quiz scores are {12, 11, 4, 6, 9, 11, 4, 6, 12, 16, 11, 10, 8, 4, 5}
Ascending order of the scores are {4, 4, 4, 5, 6, 6, 8, 9, 10, 11, 11, 11, 12, 12, 16}
If the number of data points is odd, the median is the middle data point in the list.
So, the median is 9.
To find mode:
The mode is simply the number that appears most often within a data set.
So, 4 and 11 appears 3 times in the set.

Problem Solving

Solve. Show your work.

The data set shows the amount of money 10 children spent in a week.
$16, $13, $11, $19, $17, $28, $15, $11, $13, $11

Question 4.
Find the mean and median amount of money spent.
Answer:
mean = 15.4
median = $16

Explanation:
Mean:
The sum of the values by adding them all up.
$16 + $13 + $11 + $19 + $17 + $28 + $15 + $11 + $13 + $11 = 154
Divide the sum by the number of values in the data set.
154 ÷ 10 = 15.4
Median:
Arrange the data points from smallest to largest.
Given set of quiz scores are {$16, $13, $11, $19, $17, $28, $15, $11, $13, $11}
Ascending order of the scores are {$11, $11, $11, $13, $13, $15, $16, $17, $19, $28}
If the number of data points is even, the median is the average of middle 2 data point in the list.
$13 and $15 are the middle points in the data.
13 + 15 = 28
28 ÷ 2 = 16
So, the median is $16.

Question 5.
Which amount of money would you delete from the list if you want the mean to be closer to the median? Explain your answer.
Answer:
$28

Explanation:
Amounts at the extreme have more effect on the mean than the median.
Ascending order of the scores are {$11, $11, $11, $13, $13, $15, $16, $17, $19}

Use the data in the table to answer the question.

Question 6.
Three classes in Grade 7 took a geography test last week. The table shows the mean score of the students in each class.

The mean score of the students in classes A and B combined is 7.25. The mean score of all the students in the three classes is 6.5. Find the values of x and y.
Answer:
x = 15
y = 5

Explanation:
The mean score of the students in classes A and B combined is 7.25.
The mean score of all the students in the three classes is 6.5.
The mean = \(\frac{Sum of a set of items}{Number of items}\)
7.25 = \(\frac{6× + 25×8}{25 + x}\)
60x + 200 = 7.25{25 + x}
6x + 200 =7.25x + 181.25
200 – 181.25 = 7.25-6x
18.75 = 1.25x
x = 15

Mean
15×6 + 25×8 + 20y = 6.5(15+25+20)
90+200+20y = 6.5 x 60
290 + 20y = 390
20y = 390-290
y = 100/20
y = 5

Make a dot plot to show the data. Use your dot plot to answer questions 7 and 8.

The table shows the number of goals scored by a soccer team in 15 games.

Question 7.
Find the mean, median, and mode of the data set.
Answer:
mean = 2.2
median = 2
mode = 2

Explanation:
The above tabulated data is the table shows the number of goals scored by a soccer team in 15 games.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)

mean = \(\frac{1×5 + 6×2 + 3×3 + 0×4 + 0×5 + 0×6 + 1×7}{15}\)
mean = \(\frac{5 + 12 + 9 + 7}{15}\)
mean = \(\frac{33}{15}\)
mean = 2.2
Mode
The above observations are:
1, 1, 1, 1, 1, 2, 2,2 2, 2, 2, 3, 3, 3, 7
As 2 has more number the table shows the number of goals scored by a soccer team in 15 games.
Mode is 2
Median:
The above observations are
1, 1, 1, 1, 1, 2, 2,2 2, 2, 2, 3, 3, 3, 7
total 15 observation
median : Middle value is the median of a given data set.
1, 1, 1, 1, 1, 2, 2,2 2, 2, 2, 3, 3, 3, 7
the above data has 15 observations,
2 is in the middle of the above series of numbers.
hence 2 is the median.

Question 8.
Briefly describe the data distribution and relate the measure of center to the distribution.
Answer:
The mean is to the right of the median. with mean 2.2 as peak.

Explanation:
Measures of central tendency are summary statistics that represent the center point or typical value of a dataset.
The shape of the data distribution is right skewed.
The mean gives more weight to the values on the right than the median does.
So, the mean is to the right of the median. with mean 2.2 as peak.

Use the data in the dot plot to answer questions 9 to 13.

The dot plot shows the results of a survey to find the number of computers in 30 randomly chosen families. Each dot represents 1 family.

Question 9.
What is the modal number of computers?
Answer:
2

Explanation:
The above dot plot shows the results of a survey of the number of computers in 30 randomly chosen families. Each dot represents 1 family.
8 families with 2 computes
So, the mode of the above data is 2
as 2 computers having families are more.

Question 10.
What is the mean number of computers? Round your answer to the hundredths place.
Answer:
Mean = 1.9
The nearest hundredth place is 2.

Explanation:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0×6 + 1×6 +2×8 + 3×6 + 4×4}{30}\)
mean = \(\frac{0 + 6 +16 + 18 + 16 }{30}\)
mean = \(\frac{56}{30}\)
mean = 1.9

Question 11.
What is the median number of computers?
Answer:
median = 2

Explanation:
The above observations are:
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4
total 30 observation
median : Middle value is the median of a given data set.
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4
the above data has 30 observations,
So, 2, 2 in the middle of the order sequence is the median.
the average of (2 + 2)/2 = 4/2 = 2
hence 2 is the median.

Question 12.
Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown.
Answer:
A measure of center is called a measure of central tendency of the data plot.

Explanation:
Given, The dot plot shows the results of a survey to find the number of computers in 30 randomly chosen families. Each dot represents 1 family.

Center describes a typical value of a data point.
Two measures of center are mean and median.
The shape of the data distribution is right skewed.
Hence, the mean and median are 2.

Question 13.
A similar survey is carried out on another 15 randomly chosen families and the mean number of computers is found to be 2. If the two data sets are combined, find the mean number of computers in the combined data set. Round your answer to the nearest hundredth.
Answer:
mean = 1.86
nearest hundredth = 2

Explanation:
Number of Computers in 1st set
0×6 + 1×6 +2×8 + 3×6 + 4×4 = 56
Number of families in 1st set = 30
Number of Computers in 2nd set = x
Number of families in 2nd set = 15
Mean of 2nd set = 2
mean = \(\frac{Total number of computes in 2nd set}{Total number of families}\)
2 = \(\frac{x}{15}\)
x = 30
Total number of computers = 30 + 56 = 86
Total number of families = 15 +30 = 45

mean = \(\frac{86}{45}\)
mean = 1.91
Round the answer to the nearest hundredth.
mean 1.9

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 14 Lesson 14.4 Real-World Problems: Mean, Median, and Mode detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 14 Lesson 14.4 Answer Key Real-World Problems: Mean, Median, and Mode

Math in Focus Grade 6 Chapter 14 Lesson 14.4 Guided Practice Answer Key

Solve.

The table shows the sizes of T-shirts and the number of T-shirts displayed in a shop.

Question 1.
How many T-shirts are displayed in the shop?
Answer:
60 T-shirts are displayed in the shop.

Explanation:
The above table shows the sizes of T-shirts and the number of T-shirts displayed in a shop.
Sum of the T-shirts 7 + 14 + 22 + 15 + 2 = 60
60 T-shirts are displayed in the shop.

Question 2.
What is the mean size of the T-shirts being displayed?
Answer:
11.7
Rounded to the nearest ten as 12.

Explanation:
The above table shows the sizes of T-shirts and the number of T-shirts displayed in a shop.
Mean = \(\frac{\text {The sum of the values in a data set}}{\text {The number of values in a data set}}\)
Mean = \(\frac{ 8×7+ 10×14 + 12×22 + 14×15 + 16×2}{60}\)
Mean = \(\frac{56 + 140 + 264 + 210 + 32}{60}\)
Mean = \(\frac{702}{60}\)
Mean = 11.7

Question 3.
What is the modal size of the T-shirts being displayed?
Answer:
12
Explanation:
The above table shows the sizes of T-shirts and the number of T-shirts displayed in a shop.
As more number of T shirts displayed were 12 number size.

Question 4.
What is the median size of the T-shirts being displayed?
Answer:
12

Explanation:
The above table shows the sizes of T-shirts and the number of T-shirts displayed in a shop.
We know that the median is the middle point in a dataset.
To find the median: Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
So, the median of the above set is {8, 10, 12, 14, 16} is 12.

Question 5.
Which measure of central tendency best describes the data set? Justify your answer.
Answer:
Mean

Explanation:
Mean is generally considered the measure of central tendency and the most frequently used one. The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

Solve.

The dot plot shows the results of a survey on the number of children below 13 years old in each household. Each dot represents one household.

Question 6.
Find the mean, mode, and median of the data set.
Answer:
mean = 1.6
mode = 0
median = 1

Explanation:
The above dot plot shows the results of a survey on the number of children below 13 years old in each household. Each dot represents one household.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0 + 4 + 6 + 3 + 5 + 6 }{15}\)
mean = \(\frac{24}{15}\)
mean = 1.6

Mode:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 5, 6
the above data has 15 observations,
So,  0 appears most frequently, is the mode of a given data.

Median:
median : Middle value is the median of a given data set.
0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 5, 6
the above data has 15 observations,
So, 1 in the middle of the order sequence is the median.

Question 7.
Which measure of central tendency best describes the data set? Justify your answer.
Answer:
Mean or Median measure of central tendency best describes the data set.

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
Mode is zero ‘0’, but it tells 5 children out of 15 households.
So, the mode does not describe the set of the data.
Mean is 1.6 and median is 1.
These two may be used for better answer to describe the set of data.

Question 8.
Relate the measures of center to the shape of the data distribution.
Answer:
The shape of the data distribution is right skewed.
The mean gives more weight to the values on the right than the median does.
So, the mean is to the right of the median.

Explanation:
The two main numerical measures for the center of a distribution are the mean and the median. The mean is the average value, while the median is the middle value.

Solve.

The dot plot shows the number of feedback forms received by a mall over a ten-week period. Each dot represents one feedback form.

Question 9.
Find the mean, mode, and median of the data set.
Answer:
mean = 5.4
mode = 5
median = 5

Explanation:
The above dot plot shows the number of feedback forms received by a mall over a ten-week period. Each dot represents one feedback form.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{1×1 +1×2 + 2×3 + 3×4 + 4×5 + 3×6 + 2×7 + 2×8 + 1×9 + 1×10 }{20}\)
mean = \(\frac{108}{20}\)
mean = 5.4
Mode
The above observations are
1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6,7, 7, 8, 8, 9, 10
As 5 has more number of dots in the above given dot plot : mode is 5
Median:
The above observations are
1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6,7, 7, 8, 8, 9, 10
total 20 observation
median : Middle value is the median of a given data set.
1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6,7, 7, 8, 8, 9, 10
the above data has 20 observations,
So, 5, 5 in the middle of the order sequence is the median.
the average of (5 + 5)/2 = 10/2 = 5

Question 10.
Relate the measures of center to the shape of the data distribution.
Answer:
The data are well spread out, and the shape of the data is symmetrical. Because the mode and median are the same 5 and 5 and the mean is slightly higher 5.4. The data set is likely to be more spread out for data greater then 5.

Explanation:
The two main numerical measures for the center of a distribution are the mean and the median. The mean is the average value, while the median is the middle value.

Hands-On Activity

FINDING POSSIBLE VALUES OF MEAN, MEDIAN, AND MODE

Work in pairs.

The lengths of 10 wallets have the same mean, median, and mode of 12 centimeters.

Explore and find a set of possible values for these lengths.

Show your work.
(Hint: You may use a dot plot to help you.)

Answer:
Mean = 12
Mode = 12
Median = 12

Explanation:
Given, The lengths of 10 wallets have the same mean, median, and mode of 12 centimeters.

Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{1×10 +2×11 + 4×12 + 2×13 + 1×14}{10}\)
mean = \(\frac{10 +22 + 48 + 26 + 14}{10}\)
mean = \(\frac{120}{10}\)
mean = 12
Mode:
The above observations are,
10, 11, 11, 12, 12, 12, 12, 13, 13, 14
As 12 has more number of dots in the above given dot plot : mode is 12
Median:
The above observations are,
10, 11, 11, 12, 12, 12, 12, 13, 13, 14
From the total 10 observations,
median : Middle value is the median of a given data set.
10, 11, 11, 12, 12, 12, 12, 13, 13, 14
the above data has 10 observations,
So, 12, 12 in the middle of the order sequence is the median.
the average of (12 + 12)/2 = 24/2 = 12

Math in Focus Course 1B Practice 14.4 Answer Key

Find the mean, median, and mode.

Question 1.
Eight students took a mathematics quiz. Their scores were 85, 92, 73, 85, 68, 82, 93, and 76. Find the mean, median, and mode.
Answer:
Mean = 81.75
Mode = 85
Median = 83.5

Explanation:
Eight student’s mathematics quiz scores were 85, 92, 73, 85, 68, 82, 93, and 76.
were arranged in ascending order as below.
68, 73, 76, 82, 85, 85, 92, 93
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{68 + 73 + 76 + 82 + 85 + 85 + 92 + 93}{8}\)
mean = \(\frac{654}{8}\)
mean = 81.75
Mode:
The above observations are
68, 73, 76, 82, 85, 85, 92, 93
As 85 has more number of observation : mode is 85
Median:
The above observations are
68, 73, 76, 82, 85, 85, 92, 93
total 8 observation
median : Middle value is the median of a given data set.
68, 73, 76, 82, 85, 85, 92, 93
the above data has 10 observations,
So, 82, 85 in the middle of the order sequence is the median.
the average of (82 + 85)/2 = 167/2 = 83.5

Use the data in the table to answer questions 2 and 3.

The table shows the results of a survey carried out on 80 families.

Question 2.
Find the mean, median, and mode.
Answer:
Mean = 2.4
Mode = 2
Median =2

Explanation:
The above table shows the results of a survey carried out on 80 families.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x8 +1×17 + 2×21 + 3×13 + 4×13 +5×6 + 6×2}{21}\)
mean = \(\frac{0 +17 + 42 + 39 + 52 + 30 + 12}{80}\)
mean = \(\frac{192}{80}\)
mean = 2.4
Mode:
The above observations are
0x8,1×17, 2×21, 3×13, 4×13, 5×6, 6×2
As 2 has more number observation the above given table, 21 families have 2 childrens : mode is 2
Median:
As 2 has more number observation the above given table, 21 families have 2 children : median is 2
the above data has 192 observations,
So, 2, 2 in the middle of the order sequence is the median.
the average of (2 + 2)/2 = 4/2 = 2

Question 3.
Which measure of central tendency best describes the data set? Justify your answer.
Answer:
The median and mode.

Explanation:
The mean number of children is 2.4 it is not a realistic number for describing the data set.
The median and mode are both 2, which is a realistic number for describing the data.

Solve. Show your work.

The data set shows the weights of ten gerbils in ounces.
5.49, 4.48, 4.57, 4.59, 4.61, 4.57, 4.98, 4.43, 4.45, 4.58

Question 4.
Find the mean, median, and mode.
Answer:
Mean = 4.675
Mode = 4.57
Median = 4.575

Explanation:
Given set of data, 5.49, 4.48, 4.57, 4.59, 4.61, 4.57, 4.98, 4.43, 4.45, 4.58
arrange the given data in the ascending order,
4.43, 4.45, 4.48, 4.57, 4.57, 4.58, 4.59, 4.61, 4.98, 5.49
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{4.43+ 4.45+ 4.48+ 4.57+ 4.57+ 4.58+ 4.59+ 4.61+ 4.98+ 5.49}{10}\)
mean = \(\frac{46.75}{8}\)
mean = 4.675
Mode:
The above observations are
4.43, 4.45, 4.48, 4.57, 4.57, 4.58, 4.59, 4.61, 4.98, 5.49
As 4.57 has more number of observation : mode is 4.57
Median:
median : Middle value is the median of a given data set.
4.43, 4.45, 4.48, 4.57, 4.57, 4.58, 4.59, 4.61, 4.98, 5.49
the above data has 10 observations,
So, 4.57, 4.58 in the middle of the order sequence is the median.
the average of (4.57 + 4.58)/2 = 9.15/2 = 4.575

Question 5.
Which one of the weights would you delete from the list if you want the mean to be closer to the median?
Answer:
5.49 ounce

Explanation:
5.49 oz is the separate value or higher value of the gerbil in the data set,
the weights of ten gerbils in ounces.

Use the data In the dot plot to answer questions 6 to 9.

The dot plot shows the number of hours nine students spent surfing the Internet one day. Each dot represents 1 student.

Question 6.
Find the mean, median, and mode.
Answer:
Mean = 4
Mode = 1
Median = 2

Explanation:
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{1×3 +2×2 + 3×2 + 11×1 + 12×1}{9}\)
mean = \(\frac{3 + 4 + 6 + 11 + 12}{9}\)
mean = \(\frac{36}{9}\)
mean = 4
Mode:
The above observations are,
1, 1, 1, 2, 2, 3, 3, 11, 12
As 1 has more number of dots in the above given dot plot : mode is 1
Median:
The above observations are,
1, 1, 1, 2, 2, 3, 3, 11, 12
There are total 9 observations,
median : Middle value is the median of a given data set.
1, 1, 1, 2, 2, 3, 3, 11, 12
The above data has 9 observations,
So, 2 in the middle of the order sequence is the median.

Question 7.
Give a reason why the mean is much greater than the median.
Answer:
11 and 12 are the two outliers in the above given data set.

Explanation:
The mean is affected by outliers that do not influence the mean.
Therefore, when the distribution of data is skewed in the middle,
the mean is often less than the median.
When the distribution is skewed to the right,
the mean is often greater than the median.

Question 8.
Which measure of central tendency best describes the data set?
Answer:
The median is 2 it is realistic number for describing the data set.

Explanation:
Mean is generally considered the measure of central tendency and the most frequently used one.
The median 2, which is a realistic number measure of central tendency best describes the data set.

Question 9.
Relate the measures of center to the shape of the data distribution.
Answer:
The share of the distribution is right-skewed.
So, the measure of center is likely to be 2 hours, which is in the lower range.

Explanation:
The two main numerical measures for the center of a distribution are the mean and the median. The mean is the average value, while the median is the middle value.

Use the data in the dot plot to answer the questions 6 to 9.

The dot plot shows the results of a survey on the number of brothers or sisters each student in a class has. Each dot represents 1 student.

Question 10.
Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown.
Answer:
median = 2

Explanation:
Total 32 students are there,
is unimodal and symmetrical normal distribution.
Mode of the data set is 2.
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x3 +1×6 + 2×10 + 3×9 + 4×3 + 1×5}{32}\)
mean = \(\frac{0 + 6 + 20 + 27 + 12 + 5}{32}\)
mean = \(\frac{70}{32}\)
mean = 2.1875
median : Middle value is the median of a given data set.
0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5
The above data has 32 observations,
(2+2)/2 = 4/2 = 2
So, 2 in the middle of the order sequence is the median.

Make a dot plot to show the data. Use your dot plot to answer questions 11 and 12.

A box contains cards each with a number 1, 2, 3, 4, or 5 on it. In an experiment, 20 students took turns drawing a card from the box. The number written on the card was recorded before it was put back into the box.

Alice, who was the last person to draw a card, was supposed to complete the dot plot below. However, she lost the record of the experiment’s results. All she could recall was the following information.
(i) There were twice as many cards with the number ‘3’ drawn as there were cards with the number ‘4’ drawn.
(ii) There were an equal number of cards with the numbers ‘1’ and ‘5’ drawn.
(iii) 5 cards with the number ‘2’ were drawn.
(iv) 8 students drew cards that show an even number.

Question 11.
Copy and complete the dot plot.

Answer:

Explanation:
Given that,
A box contains cards each with a number 1, 2, 3, 4, or 5 on it.
20 students took turns drawing a card from the box.
The number written on the card was recorded before it was put back into the box.
Alice, who was the last person to draw a card, was supposed to complete the dot plot below. However, she lost the record of the experiment’s results.
All she could recall was the following information.
(i) There were twice as many cards with the number ‘3’ drawn as there were cards with the number ‘4’ drawn.
So, there are 6 cards with number 3.
(ii) There were an equal number of cards with the numbers ‘1’ and ‘5’ drawn.
(iii) 5 cards with the number ‘2’ were drawn.
(iv) 8 students drew cards that show an even number.
So, the even number cards are 2 and 4.

Question 12.
Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown.
Answer:
Mode of the above data is 3.
Mean is 1.1825.

Explanation:
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{1×3 +2×5 + 3×6 + 4×3 + 5×3}{20}\)
mean = \(\frac{3 + 10 + 18 + 12 + 15}{20}\)
mean = \(\frac{58}{32}\)
mean = 1.1825
median : Middle value is the median of a given data set.
1,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,5,5
The above data has 20 observations,
(3+3)/2 = 6/2 = 3
So, 3 in the middle of the order sequence is the median.

Use the data in the table to answer questions 13 to 17.

The table shows the number of students absent from school over a 30-day period.

Question 13.
What is the mode of this distribution?
Answer:
mode = 2

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
So, 2 is most frequent appearance,
it means 10days out of 30 days 2 students are absent.

Question 14.
Find the mean and median number of students absent from school over the 30 days.
Answer:
Mean = 1.4
Median = 2

Explanation:
Mean:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x8 + 1×7 + 2×10 + 3×5}{30}\)
mean = \(\frac{0 + 7 + 20 + 15}{30}\)
mean = \(\frac{42}{30}\)
mean = 1.4
median : Middle value is the median of a given data set.
0, 0, 0, 0, 0, 0, 0, 0, 7, 2. 2. 2. 2. 2. 2. 2. 2. 2. 2, 10, 5, 5, 5
The above data has 30 observations,
(2+2)/2 = 4/2 = 2
So, 2 in the middle of the order sequence is the median.

Question 15.
It is found that the mean number of students absent from school over a subsequent 20-day period is 1. Find the mean number of students absent from school over the entire 50-day period.
Answer:
1.24

Explanation:

The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x8 + 1×27 + 2×10 + 3×5}{30}\)
mean = \(\frac{0 + 27 + 20 + 15}{30}\)
mean = \(\frac{62}{50}\)
mean = 1.24

Question 16.
If on one day of the 30-day period, 4 students were absent from school instead of 3, what should the mean of the distribution over the first 30-day period be? Round your answer to the nearest hundredth.
Answer:
1.57

Explanation:

The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{0x8 + 1×7 + 2×10 + 4×5}{30}\)
mean = \(\frac{0 + 7 + 20 + 20}{30}\)
mean = \(\frac{47}{30}\)
mean = 1.566666
Round the answer to the nearest hundredth.
1.57

Question 17.
If on one day of the 30-day period, 2 students were absent from school instead of 1, would the median of the distribution over the 30-day period be affected? If so, what is the new median?
Answer:
Yes,
So, median is 2

Explanation:

median : Middle value is the median of a given data set.
0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2. 2. 2. 2. 2. 2. 2. 2. 2. 2, 10, 5, 5, 5
The above data has 30 observations,
So, 2 in the middle of the order sequence is the median.

Brain @ Work

In a series of six class quizzes, Tim’s first four quiz scores are 3, 5, 6, and 8. The mean score of the six quizzes is 6. If the greater of the missing quiz scores is doubled, the mean score becomes 7\(\frac{1}{3}\). What are the two missing quiz scores?

Answer:
5th test score = 8
6th test score = 6

Explanation:
In a series of six class quizzes, Tim’s first four quiz scores are 3, 5, 6, and 8.
The mean score of the six quizzes is 6.
Let fifth test scores = x
sixth test scores = y
mean = (3 + 5 + 6 + 8 + x + y) ÷ 6= (22 + x + y) ÷ 6
(22 + x + y)÷ 6 = 6
22 + x + y = 36
x + y = 36 – 22
x + y = 14
y = 14 – x
if the high test test scores are doubled,
(3 + 5 + 6 + 8 + 2x + y) ÷ 6= (22 + 2x + y) ÷ 6
(22 + 2x + y)÷ 6 = 7\(\frac{1}{3}\)
22 + 2x + y = 7\(\frac{1}{3}\) x 6
2x + y = 44 – 22
2x + 14 – x = 22
x = 22 – 14
x = 8
So, y = 14 – x
y = 14 – 8
y = 6
Hence, 5th test score = 8
Hence, 6th test score = 6

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 14 Lesson 14.3 Mode detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 14 Lesson 14.3 Answer Key Mode

Math in Focus Grade 6 Chapter 14 Lesson 14.3 Guided Practice Answer Key

Use the data set to complete the table. Then complete the sentence.

Justin recorded the times for the ten runners on a track team when they ran the 100-meter dash. The data set shows the times that he recorded.

9.8 s, 9.9 s, 10.0 s, 9.9 s, 10.2 s, 10.1 s, 9.8 s, 10.3 s, 9.9 s, 10.1 s

Answer:

Explanation:
Given that,
Justin recorded the times for the ten runners on a track team when they ran the 100-meter dash. The data set shows the times that he recorded as..
9.8 s, 9.9 s, 10.0 s, 9.9 s, 10.2 s, 10.1 s, 9.8 s, 10.3 s, 9.9 s, 10.1 s
Number of times of ten runners are recorded in the table as shown above.

Question 1.
The mode of this data set is seconds.
Answer:
9.9 seconds.

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
So, it is the third measure of the central tendency.
9.9s occurs the maximum number of times in a given data set.

Complete. Use data in the dot plot.

Elsie likes to bowl. The dot plot shows her scores for each of the ten frames that she bowled in one game. Each dot represents her scores for one frame.

Question 2.
Elsie scored 11 points in each of frames.
Answer:
2 frames.

Explanation:
A Dot Plot is a graphical display of data using dots.
As each dot represents her scores for one frame, there are 2 dots at 11 points.
So, Elsie scored 11 points in each of 2 frames.

Question 3.
The modes of this set of data are and .

Answer:
8, 12 are the modes.

Explanation:
The above dot plot shows her scores for each of the ten frames that she bowled in one game. Each dot represents her scores for one frame.
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
Three are 3 frames at 8 and three frames at the 12 point.
So, 3 is occurring more number of times.

Find the mode of each set of data.

Question 4.
There are 9 teachers, 88 boys, and 79 girls at a school camp.
Answer:
mode = boys.

Explanation:
Given that,
There are 9 teachers, 88 boys, and 79 girls at a school camp.
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
As boys are more number, which can see frequently more number of times.
So, in the above set of data boys are mode.

Question 5.
In a mall, there are 2 laundry shops, 14 garment shops, 3 photographic shops, 5 shoe shops, and 9 food stores.
Answer:
mode is garment shop.

Explanation:
Given that,
In a mall, there are 2 laundry shops, 14 garment shops, 3 photographic shops, 5 shoe shops, and 9 food stores.
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
As garment shops are more number, which can see frequently more number of times.
So, garment shop is mode.

Question 6.
The data set shows the masses of the school bags of some students.
5.5 kg, 6.6 kg, 4.8 kg, 4.3 kg, 5.5 kg, 4.3 kg, 5.5 kg, 6.6 kg, 4.5 kg, 5.5 kg
Answer:
mode is 5.5kg

Explanation:
Given that,
5.5 kg, 6.6 kg, 4.8 kg, 4.3 kg, 5.5 kg, 4.3 kg, 5.5 kg, 6.6 kg, 4.5 kg, 5.5 kg is to be written in the ascending order.
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
4.3, 4.3, 4.5, 4.8, 5.5, 5.5, 5.5, 5.5, 6.6, 6.6
So, 5.5 is more times observation is the mode of the given set of data.

Hands-On Activity

FINDING MEAN, MEDIAN, AND MODE

Materials:

• net of a rectangular prism, with pairs of opposite faces numbered 10, 11, or 12
• blank table
• tape
• scissors
• centimeter ruler

Work in pairs.
Step 1: Cut out, fold, and tape the net of the rectangular prism provided by your teacher.
Step 2: Take turns to toss the rectangular prism 40 times and record the number tossed each time.
Step 3: Copy and complete your results in a table like the one below.

Step 4: From the set of data collected, find the
a) mean
b) median
c) mode.

Step 5:
a) Measure the area of each face to the nearest tenth of a square centimeter. Find the ratio of the total area of the faces numbered 10 to the total area of the faces numbered 11 to the total area of the faces numbered 12.
b) Find the ratio of the number of times the number 10 is tossed to the number of times the number 11 is tossed to the number of times the number 12 is tossed.
c) Compare the two ratios. Why do you think you get this result?

Step 6: Compare your findings with the other pairs.
Answer:

the ratio of the number of times the number 10 is tossed to the number of times the number 11 is tossed to the number of times the number 12 is tossed
10:11:12
9 : 16 : 15

Math in Focus Course 1B Practice 14.3 Answer Key

Find the mode or modes of each data set.

Question 1.
5, 6, 4, 5, 8, 9, 9, 3, 4, 5
Answer:
Mode : 5

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
Given 5, 6, 4, 5, 8, 9, 9, 3, 4, 5
The given data set is to be written in the ascending order.
3, 4, 4, 5, 5, 5, 6, 8, 9, 9
So, number 5 appears most frequently in the given set of data.

Question 2.
13, 31, 12, 45, 6, 19, 21, 12, 31
Answer:
12 and 31

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
Given 13, 31, 12, 45, 6, 19, 21, 12, 31
The given data set is to be written in the ascending order.
6, 12, 12, 13, 19, 21, 31, 31, 45
So,12 and 31 appears most frequently in the given set of data.

Question 3.
8.5, 6.5, 7.8, 6.5, 6.4, 2.3, 4.5, 5.4, 7.8, 5.5, 7.8
Answer:
7.8

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
Given 8.5, 6.5, 7.8, 6.5, 6.4, 2.3, 4.5, 5.4, 7.8, 5.5, 7.8
The given data set is to be written in the ascending order.
2.3, 4.5, 5.4, 5.5, 6.4, 6.5, 6.5, 7.8, 7.8, 7.8, 8.5
So, 7.8 appears most frequently in the given set of data.

Find the mode.

Question 4.
The scores of a basketball team in a series of games are 76, 85, 65, 58, 68, 72, 91, and 68. Find the mode.
Answer:
mode is 65

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
Given 76, 85, 65, 58, 68, 72, 91, and 68
arranging in the ascending order
58, 65, 68, 68, 72, 76, 85, 91
So, 68 appears most frequently in the given set of data.

Question 5.
The table shows sizes of shoes and the number of pairs of shoes sold at a shop last month.

Find the mode.
Answer:
30

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
The above number of pairs of shoes sold are arranged in the ascending order as shown below.
3, 5, 8, 13, 15, 21, 30, 30, 31
In the above 9 observations of 30 is occurred more number of times.
So, mode =  30

Question 6.
Tickets for a concert are priced at $20, $30, $40, $50, or $100. The table shows the number of tickets sold at each price.

Find the mode.
Answer:
mode = 40

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
So, $40 is 95 tickets were sold, $40 appears most frequently.

Make a dot plot to show the data. Use your dot plot to answer each question.

The data set shows the number of goals scored by a soccer team in 17 matches. 3, 2, 1, 0, 2, 4, 1, 0, 2, 3, 4, 2, 3, 2, 1, 2, 5
Question 7.
What is the mean of the data set? Round your answer to the nearest number of goals.
Answer:
mean = 2
2 goals.

Explanation:
Given, 3, 2, 1, 0, 2, 4, 1, 0, 2, 3, 4, 2, 3, 2, 1, 2, 5
find the sum of the above data,
3+2+1+0+2+4+1+0+2+3+4+2+3+2+1+2+5 = 37
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{3+2+1+0+2+4+1+0+2+3+4+2+3+2+1+2+5}{17}\)
mean = \(\frac{37}{17}\)
mean = 2.17
Round the answer to the nearest number of 2 goals.

Question 8.
What is the median of the data set?
Answer:
median =2

Explanation:
median: Middle value is the median of a given data set.
3, 2, 1, 0, 2, 4, 1, 0, 2, 3, 4, 2, 3, 2, 1, 2, 5
The above data is arranged in ascending order as shown below,
0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5
So, 2 in the middle of the order sequence is the median.

Question 9.
What is the mode of the data set?
Answer:
mode = 2

Explanation:
Mode is the value which occurs the maximum number of times in a given data set.
It is the third measure of the central tendency.
3, 2, 1, 0, 2, 4, 1, 0, 2, 3, 4, 2, 3, 2, 1, 2, 5
The above data is arranged in ascending order as shown below,
0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5
So, 2 appears most frequently in the given set of data.

Solve. Show your work.

Question 10.
A class of 15 students had a spelling test consisting of 10 words. The number of spelling mistakes made by each student in the class is listed in the data set.
1, 2, 1, 0, 3, 1, 2, 3, 1, 2, 0, 4, 2, 3, x
a) If there are two modes, what are the possible values for x?
Answer:
x = 0 and 4

Explanation:
Given, 1, 2, 1, 0, 3, 1, 2, 3, 1, 2, 0, 4, 2, 3, x
arrange the data in the ascending order,
0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, x
there are two modes,
As 1 and 2 appears most frequently in the given set of data.
So, the possible values of x is 0 and 4.

b) If there is exactly one mode, write a possible value for x, and the mode.
Answer:
1 or 2

Explanation:
Given set of data,
1, 2, 1, 0, 3, 1, 2, 3, 1, 2, 0, 4, 2, 3, x
arrange the data in the ascending order,
0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 1
if the possible values for x = 1
As 1 appears most frequently in the given set of data,
mode is 1
if the possible values for x = 2
As 2 appears most frequently in the given set of data,
mode is 2.

Question 11.
The table shows the number of days of absences for 80 students in a school.

a) Find the value of x + y.
Answer:
30

Explanation:
As we know total number of students is 80 in the school.
x + 25 + 17 + y + 8 = 80
x + y = 80 – 50
x + y = 30

b) If the mode for this set of data is 3, write the possible values for the pair of numbers (x, y).
Answer:
(x, y)

Explanation:
x + 25 + 17 + y + 8 = 80
x + y = 80 – 50 = 30
we know total students are 80.
3 is mode, means y value should maximum value and x value should me minimum.
The sum of x + y = 30
(x, y) = (0, 30), (1, 29), (2, 28), (3, 27), (4, 26)
So, the possible values of the pair of numbers (x, y).

c) If the mode is equal to the median, write two possible values of x.
Answer:
25 and 27

Explanation:
median : Middle value is the median of a given data set.
x, 25, 17, y, 8
arrange the data in the ascending order,
8, 17, 25, x y
So, the possible numbers between are 16 to 24.
So, mode should be 25 and 17 if any one same numbers repeats.

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 14 Lesson 14.2 Median detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 14 Lesson 14.2 Answer Key Median

Math in Focus Grade 6 Chapter 14 Lesson 14.2 Guided Practice Answer Key

Find the median of each data set.

Question 1.
The data set shows the weights of a group of students.
109 lb, 86 lb, 117 lb, 97 lb, 98 lb
Ordered from least to greatest:
lb, Ib, lb, lb, lb
The median weight is ____ pounds.
Answer:
98 lb

Explanation:
It is given that the data set shows the weights of a group of students.
109 lb, 86 lb, 117 lb, 97 lb, 98 lb
Now, arrange the given weights of the group of students from the least to the greatest.
So, the order of the weights from the least to the greatest is:
86 lb, 97 lb, 98 lb, 109 lb, 117 lb
Now, from the given data set,
The number of given weights is: 5
We know that, when a data set has an odd number of values,
you can identify the middle value or median by inspection.
So, the median of the given data set is: 98 lb
Hence, the median weight is 98 lb.

Question 2.
The data set shows the volumes of water (in fluid ounces) in some containers.

The median volume of water is _____fluid ounces.
Answer:
32 fluid ounces.

Explanation:
It is given that the data set shows the volumes of water (in fluid ounces) in some containers.

Now from the above containers we can observe that,
The volumes of water in the given containers are:
16 fluid ounces, 32 fluid ounces, 56 fluid ounces, 8 fluid ounces, 64 fluid ounces.
The volumes of water in the given containers from the least to the greatest are:
8 fluid ounces, 16 fluid ounces, 32 fluid ounces, 56 fluid ounces, 64 fluid ounces.
So, the number of volumes of water in the given containers is: 5
We know that when a data set has an odd number of values,
you can identify the middle value or median by inspection
So, the median volume of water is: 32 fluid ounces.

Question 3.
The data set shows the ages of a group of people.
23 years, 36 years, 28 years, 43 years, 34 years, 29 years
The two middle values are ______ years and ______ years.
Mean of the two middle values =
The median age is ______ years.
Answer:
31.5 years.

Explanation:
It is given that the data set shows the ages of a group of people.
23 years, 36 years, 28 years, 43 years, 34 years, 29 years.
Now arrange the ages of a group of people from the least to the greatest are:
23 years, 28 years, 29 years, 34 years, 36 years, 43 years.
We know that when a data set has an even number of values, identify the two middle values.
The median is the mean of these two middle values.
Now, the number of values present in a data set is: 6
So, the mean of the two middle values = \(\frac{29 + 34}{2}\)
= \(\frac{63}{2}\)
= 31.5 years
Hence, the median age is 31.5 years.
Question 4.

The data set shows the lengths of the tables that one company produces.
85 cm, 92 cm, 108 cm, 210 cm, 264 cm, 200 cm, 135 cm, 78 cm
The median length is centimeters.
Answer:
121.5 years.

Explanation:
It is given that the data set shows the lengths of the tables that one company produces.
85 cm, 92 cm, 108 cm, 210 cm, 264 cm, 200 cm, 135 cm, 78 cm
Now arrange the lengths of the tables from the least to the greatest are:
78 cm, 85 cm, 92 cm, 108 cm, 135 cm, 200 cm, 210 cm, 264 cm
We know that when a data set has an even number of values, identify the two middle values.
The median is the mean of these two middle values.
So, the number of values present in a data set is: 8
The mean of the two middle values = \(\frac{108 + 135}{2}\)
= \(\frac{243}{2}\)
= 121.5 years
Hence, the median length is 121.5 years.

Question 5.
The data set shows the distances that a group of students ran during an exercise.
\(\frac{1}{2}\) mi, \(\frac{7}{8}\) mi, \(\frac{3}{4}\) mi, \(\frac{5}{8}\) mi
The median distance was ___ miles.
Answer:
\(\frac{11}{16}\) miles

Explanation:
It is given that the data set shows the distances that a group of students ran during an exercise.
\(\frac{1}{2}\) mi, \(\frac{7}{8}\) mi, \(\frac{3}{4}\) mi, \(\frac{5}{8}\) mi
Now arrange the distance that a group of students ran during an exercise from the least to the greatest is:
\(\frac{1}{2}\) mi, \(\frac{5}{8}\) mi, \(\frac{3}{4}\) mi, \(\frac{7}{8}\) mi
We know that when a data set has an even number of values, identify the two middle values.
The median is the mean of these two middle values
So, the number of values present in a data set is: 4
The mean of the two middle values = (\(\frac{5}{8}\) + \(\frac{3}{4}\)) × \(\frac{1}{2}\)
= \(\frac{11}{8}\) × \(\frac{1}{2}\)
= \(\frac{11}{16}\) mi
Hence, the median distance is \(\frac{11}{16}\) miles.

Complete. Use the data in the dot plot.

The dot plot shows the weights of a group of immature white-tailed deer fawns. Each dot represents 1 fawn.

Question 6.
The median weight of the fawns is _____ pounds.
Answer:
100 pounds.

Explanation:
It is given that the dot plot shows the weights of a group of immature white-tailed deer fawns and each dot represents 1 fawn.
The given dot plot is:

We observe that, the total number of fawns is: 7
Now arrange the order of the fawns from the least to the greatest is:
1 fawn, 1 fawn, 1 fawn, 2 fawns, 2 fawns
We know that when a data set has an odd number of values,
you can identify the middle value or median by inspection.
So, the median weight of the fawns = The middle value of the weights of a group of immature white-tailed deer fawn.
= 100 × (The number of fawns corresponding to the weight of 100 lb)
= 100 × 1
= 100 lb
Hence, the median weight of the fawns is 100 pounds.

Question 7.
A new fawn joins the group. It weighs 101 pounds.
a) Add a dot to a copy of the dot plot above to show this information.
Answer:

Explanation:
It is given that the dot plot shows the weights of a group of immature white-tailed deer fawns and each dot represents 1 fawn.
The given dot plot is:

A new fawn joins the group.
It weighs 101 pounds.
Hence, The dot plot that represents the given information is shown above.

b) Does this change the median of the data set? What is the median of the data set now?
Answer:
100.5 pounds.

Explanation:
From part (a), we can observe that
The new dot plot is:

Since the dots (The number of fawns) are changed, the median of the data set will also be changed.
Since the number of fawns is even, the median will be the middle value of the 4th and 5th values.
So, the median of the new data set = \(\frac{101 + 100}{2}\)
= \(\frac{201}{2}\)
= 100.5 pounds
Hence, the median of the data set now will be 100.5 pounds.

Complete. Use the data in the dot plot.

The lowest temperatures in a town are recorded over a few days. The dot plot on the right shows these temperature readings. Each dot represents 1 temperature reading.

Question 8.
The mean temperature is °F.
Answer:
45.5 °F

Explanation:
It is given that the lowest temperatures in a town are recorded over a few days.
The dot plot on the right shows these temperature readings.
Each dot represents 1 temperature reading.
The given data plot is:

We know that,
Mean = \(\frac{\text {The sum of the values in a data set}}{\text {The number of values in a data set}}\)
From the given data plot we observe that,
The number of values in the given data set is: 8
So, Mean temperature = \(\frac{(40 × 1) + (41 × 1) + (46 × 2) + (47 × 1) + (48 × 3)}{8}\)
= \(\frac{40 + 41 + 92 + 47 + 144}{8}\)
= \(\frac{364}{8}\)
= 45.5°F
Hence, the mean temperature is 45.5 °F.

Question 9.
The median temperature is °F.
Answer:
44 °F

Explanation:
It is given that the lowest temperatures in a town are recorded over a few days.
The dot plot on the right shows these temperature readings.
Each dot represents 1 temperature reading.
The given data plot is:

From the above dot plot we observe that,
The total number of temperature readings is 8.
So, Median = The middle value of the temperature readings.
Hence, The median temperature is 44 °F.

Question 10.
of the temperature readings recorded are higher than the mean temperature.
Answer:
46 °F, 47 °F, and 48 °F

Explanation:
It is given that the lowest temperatures in a town are recorded over a few days.
The dot plot on the right shows these temperature readings.
Each dot represents 1 temperature reading.
The given dot plot is:

From Question 8, we observe that,
The mean temperature is 45.5 ° F.
Hence, the temperature recordings that are higher than the mean temperature are 46 °F, 47 °F, and 48 °F.

Question 11.
Which of the two measures of central tendency, the mean or the median, better describes the data set? Justify your answer.
Answer:
The median describes the given data set better.

Explanation:
From Question 8 and Question 9,
We can observe that,
The mean is 45.5 °F. However, more than 1 temperature reading is less than 45.5 °F.
So, the mean does not describe the data set well.
The median is 44 °F.
It describes the data set better because most of the data values cluster around 44 °F.
Hence, the median describes the given data set better.

Hands-On Activity

COLLECTING AND TABULATING DATA TO FIND MEDIAN

Materials

• blank table

Work in pairs.

Step 1: Refer to the first paragraph of the chapter opener. Count the number of times the letter ‘e’ appears in each line. Record your answers in a copy of the table below.

Answer:

Step 2: Find the mean and median number of times the letter ‘e’ appears in each line.
Answer:
mean =7.833
median = 8.5

Explanation:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{11 + 10 + 8 + 3 + 9 + 6}{6}\)
mean = 7.833
median : Middle value is the median of a given data set.
The given data set {3, 6, 8, 9, 10, 11} contains even number and 8 and 9 are in the middle.
the average of the 8 and 9 is the median of the given data set.
median = \(\frac{8 + 9}{2}\)
median = 8.5

Math in Focus Course 1B Practice 14.2 Answer Key

Find the median of each data set.

Question 1.
9, 8, 7, 11, 7, 16, 3
Answer:
median = 8

Explanation:
median : Middle value is the median of a given data set.
The given data set {9, 8, 7, 11, 7, 16, 3}contains odd numbers.
So, arrange them in ascending order {3, 7, 7, 8, 9, 11, 16} to find the median.
Number 8 in the middle of the order sequence is the median.

Question 2.
31, 43, 12, 25, 54, 18
Answer:
median = 18.5

Explanation:
median : Middle value is the median of a given data set.
The given data set {12, 18, 25, 31, 43, 54} contains even number and are arranged in the ascending order.
12 and 25 are in the middle.
the average of the 12 and 25 is the median of the given data set.
median = \(\frac{12 + 25}{2}\)
median = \(\frac{37}{2}\)
median = 18.5

Question 3.
3.2, 1.5, 2.6, 3.5, 6.9, 5.8, 2.4
Answer:
median = 3.2

Explanation:
median : Middle value is the median of a given data set.
The given data set {3.2, 1.5, 2.6, 3.5, 6.9, 5.8, 2.4} contains odd numbers.
Arrange them in ascending order{1.5, 2.4, 2.6, 3.2, 3.5, 5.8, 6.9} to find the median.
So, 3.2 in the middle of the order sequence is the median.

Question 4.
32.6, 72.6, 28.7, 45.4, 83.6, 69.9
Answer:
median = 57.65

Explanation:
median : Middle value is the median of a given data set.
The given data set {32.6, 72.6, 28.7, 45.4, 83.6, 69.9} contains even numbers.
Arrange the numbers in the ascending order{28.7, 32.6, 45.4, 69.9, 72.6, 83.6} to fid the median.
So, the numbers 45.4 and 69.9 are in the middle.
Take the average of the 45.4 and 69.9 is the median of the given data set.
median = \(\frac{45.4 + 69.9}{2}\)
median = \(\frac{115.3}{2}\)
median = 57.65

Solve. Show your work.

Question 5.
The number of points scored by seven students in a language test are 68, 46, 74, 58, 63, 91, and 85. Find the median score.
Answer:
median = 68

Explanation:
median : Middle value is the median of a given data set.
The given data set {68, 46, 74, 58, 63, 91, 85} contains odd numbers.
Arrange the given data in ascending order {46, 58, 63, 68, 74, 85, 91} to find the median.
So, number 68 in the middle of the order sequence is the median.

Question 6.
The data set shows the number of goals scored by a soccer team in eight matches.
0, 2, 3, 1, 4, 2, 5, 2
Find the median number of goals scored.
Answer:
median = 57.65

Explanation:
median : Middle value is the median of a given data set.
The given data set {0, 2, 3, 1, 4, 2, 5, 2} contains even numbers.
Arrange the given data in ascending order {0, 1, 2, 2, 2, 3, 5} to find the median.
So, the numbers 2 and 2 are in the middle.
Take the average of the 2 and 2 is the median of the given data set.
median = \(\frac{2 + 2}{2}\)
median = \(\frac{4}{2}\)
median = 2

Question 7.
The costs of four cell phones are $345, $400, $110, and $640. Find the median cost.
Answer:
median = 372.5

Explanation:
median : Middle value is the median of a given data set.
The given data set {$345, $400, $110, and $640} contains even numbers.
Arrange the given data set in ascending order {$110, $345, $400, $640} to find the median.
So, the numbers $345 and $400 are in the middle.
Take the average of the 345 and 400 is the median of the given data set.
median = \(\frac{345 + 400}{2}\)
median = \(\frac{745}{2}\)
median = 372.5

Question 8.
The volumes of water, in liters, in eight containers are 3.1, 2.8, 3.2, 4.2, 3.9, 5.6, 3.7, and 4.5. Find the median volume.
Answer:
median = 3.8

Explanation:
median : Middle value is the median of a given data set.
The given data set {3.1, 2.8, 3.2, 4.2, 3.9, 5.6, 3.7, 4.5} contains even numbers.
Arrange the given data set in ascending order {2.8, 3.1, 3.2, 3.7, 3.9, 4.2, 4.5, 5.6}
So, the numbers 3.7 and 3.9 are in the middle.
Take the average of the 3.7 and 3.9 is the median of the given data set.
median = \(\frac{3.7 + 3.9}{2}\)
median = \(\frac{7.6}{2}\)
median = 3.8

Use the data in the dot plots to answer questions 9 and 10.

The dot plot shows the number of points scored by the members of a Quiz Bowl team in a competition between School A and School B. Each dot represents one student’s points.

Question 9.
How many team members did each school have?
Answer:
School A have 5 members.
School B have 8 members.

Explanation:
The above dot plot shows the number of points scored by the members of a Quiz Bowl team in a competition between School A and School B.
Each dot represents one student’s points.
So, count the dots on the plot of School A and School B.
School A have 5 members.
School B have 8 members.

Question 10.
What was the median number of points scored by the students from
a) School A?
Answer:
median = 2

Explanation:

median : Middle value is the median of a given data set.
The given data set {1, 1, 2, 2, 3} contains odd numbers and are arranged in the ascending order and 2 is in the middle of the order sequence.
median = 2

b) School B?
Answer:
median = 3.8

Explanation:

median : Middle value is the median of a given data set.
The given data set {1, 2, 2, 2, 3, 3, 3, 4} contains even number and are arranged in the ascending order.
2 and 3 are in the middle.
the average of the 2 and 3 is the median of the given data set.
median = \(\frac{2 + 3}{2}\)
median = \(\frac{5}{2}\)
median = 2.5

Use the data In the dot plot to answer questions 11 to 13.

Janice bought some dinner rolls from a bakery. The dot plot shows the prices of the dinner rolls in cents. Each dot represents 1 dinner roll.

Question 11.
What is the mean price of the dinner rolls Janice bought? Round your answer to the nearest cent.
Answer:
104 cents.

Explanation:
The mean = \(\frac{Sum of a set of items}{Number of items}\)
mean = \(\frac{50 + 90 + 100 + 100 + 110 + 110 + 110 +110 + 110 + 120 + 120 + 120}{12}\)
mean = 104.2
Round the answer to the nearest cent. = 104

Question 12.
What is the median price of the dinner rolls she bought?
Answer:
$110

Explanation:
median : Middle value is the median of a given data set.
The given data set {50, 90,100, 100, 110, 110, 110, 110, 110, 120, 120, 120} contains even number and are arranged in the ascending order.
110 and 110 are in the middle.
the average of the 110 and 110 is the median of the given data set.
median = \(\frac{110 + 110}{2}\)
median = \(\frac{220}{2}\)
median = 110

Question 13.
Which of the two measures of central tendency, the mean or the median, better describes the data set? Justify your answer.
Answer:
Median

Explanation:
median : Middle value is the median of a given data set.
The given data set {50, 90,100, 100, 110, 110, 110, 110, 110, 120, 120, 120} contains even number and are arranged in the ascending order.
In this situation, we would like to have a better measure of central tendency.

Solve.

Question 14.
The median of a set of numbers is x. There are at least three numbers in the set. Write an algebraic expression, in terms of x, to represent the median of the new set of numbers obtained by

a) adding 3 to every number in the set.
Answer:
x+2, x+3, x+4

Explanation:
Given that,
The median of a set of numbers is x.
There are at least three numbers in the set.
x-1, x, x+1
x-1+3, x+3, x+1+3
x+2, x+3, x+4

b) doubling every number in the set.
Answer:
2x-2, 2x, 2x+2

Explanation:
Given that,
The median of a set of numbers is x.
There are at least three numbers in the set.
x-1, x, x+1
By doubling every number in the set we get,
2x-2, 2x, 2x+2

c) dividing every number in the set by 5 and then subtracting 2 from the resulting numbers.
Answer:
((x-1)/5) – 2, (x/5) – 2, ((x+1)/5) – 2

Explanation:
Given that,
The median of a set of numbers is x.
There are at least three numbers in the set.
x-1, x, x+1
By dividing every number in the set by 5 and then subtracting 2 from the resulting numbers.
((x-1)/5) – 2, (x/5) – 2, ((x+1)/5) – 2

d) adding 2 to the greatest number in the set.
Answer:
x-1, x, x+3

Explanation:
Given that,
The median of a set of numbers is x.
There are at least three numbers in the set.
x-1, x, x+1
By adding 2 to the greatest number in the set.
x-1, x, x+1+2
So, x-1, x, x+3

e) subtracting 3 from the least number in the set.
Answer:
x-4, x, x+1

Explanation:
Given that,
The median of a set of numbers is x.
There are at least three numbers in the set.
x-1, x, x+1
subtracting 3 from the least number in the set.
x-1, x, x+1
x-1-3, x, x+1
x-4, x, x+1

Question 15.
The median of a set of three unknown numbers is 5. If the number 3 is added to the least number in the set, give an example of the original set in which
a) the median of the new set of numbers will not be equal to 5.
Answer:
Answer vary.
4, 5, 6 is the sample.

Explanation:
x-1, x, x+1
The median of a set of three unknown numbers is 5.
If the number 3 is added to the least number in the set.
x = 5
x-1, x, x+1
4, 5 , 6
If the number 3 is added to the least number in the set.
Give an example of the original set in which,
4+3, 5 , 6
5, 6 , 7

b) the median of the new set of numbers will still be equal to 5.
Answer:
No

Explanation:
We know that the median is the middle point in a dataset.
To find the median: Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
So, the median of the above set is {5, 6 , 7} is 6.

Question 16.
The median of a set of three unknown numbers is 5. If the number 2 is subtracted from the greatest number in the set, give an example of the original set in which
a) the median of the new set of numbers will not be equal to 5.
Answer:
No

Explanation:
a) the median of the new set of numbers will not be equal to 5.
x-1, x, x+1
The median of a set of three unknown numbers is 5
4, 5, 6
If the number 2 is subtracted from the greatest number in the set,
So, the greatest number is 6.
4, 5, 6-2
4, 4, 5
We know that the median is the middle point in a dataset.
To find the median: Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
Hence, median is 4.

b) the median of the new set of numbers will still be equal to 5.
Answer:
No

Explanation:
After rearranging the numbers in ascending order,
median is 4 as shown above.

This handy Math in Focus Grade 6 Workbook Answer Key Chapter 14 Lesson 14.1 Mean detailed solutions for the textbook questions.

Math in Focus Grade 6 Course 1 B Chapter 14 Lesson 14.1 Answer Key Mean

Math in Focus Grade 6 Chapter 14 Lesson 14.1 Guided Practice Answer Key

Complete.

Four boys have heights of 154 centimeters, 157 centimeters, 160 centimeters, and 165 centimeters.

Question 1.
What is the total height of the four boys?
Total height
= + + +
= cm
The total height of the four boys is ______ centimeters.
Answer:
636 centimeters.

Explanation:
It is given that four boys have heights of 154 centimeters, 157 centimeters, 160 centimeters, and 165 centimeters.
We know that, Total height of four boys = The sum of the heights of each boy.
So, The total height of the four boys = 154 cm + 157 cm + 160 cm + 165 cm = 636 cm
Hence, We can conclude that,
The total height of the four boys is 636 centimeters.

Question 2.
What is the mean height of the four boys?
Mean height
= \(\frac{\text { total height }}{\text { number of boys }}\)
= ÷
= cm
The mean height of the four boys is ______ centimeters.
Answer:
159 centimeters.

Explanation:
From Question 1, We can observe that,
The total height of the four boys is 636 centimeters
Now, We know that,
The mean height of the four boys = \(\frac{\text {The total height of four boys}}{\text {The number of boys}}\)
So, The mean height of the four boys = \(\frac{636}{4}\)
= 636 ÷ 4
Now, by using the Long Division,

Hence, from the above,
We can conclude that the mean height of the four boys is: 159 centimeters.

Complete. Use the data in the table.

The table shows the temperature at noon from Monday to Friday in one city.

Question 3.
What was the mean temperature at noon from Monday to Friday?
Mean temperature

The mean temperature at noon from Monday to Friday was °F.
Answer:
50.8°F

Explanation:
The given table is:

We know that,
Mean = \(\frac{\text {The sum of the values}}{\text {The number of values}}\)
So, The mean temperature at noon from Monday to Friday = \(\frac{52°F + 51°F + 49°F + 48°F + 54°F}{5}\)
= \(\frac{254°F}{5}\)
Now, by using the Long Division,

Hence, from the above,
We can conclude that the mean temperature at noon from Monday to Friday was 50.8°F

Complete. Use the data in the dot plot.

A group of volunteers was selling coupons to raise money for a food pantry. The dot plot on the right shows the number of coupons sold by each volunteer. Each dot represents 1 volunteer.

Question 4.
volunteers sold 8 coupons each. × = coupons sold
Answer:
24 coupons sold.

Explanation:
It is given that, A group of volunteers was selling coupons to raise money for a food pantry.
The dot plot shows the number of coupons sold by each volunteer. Each dot represents 1 volunteer.
Now, The given figure is:

From the given figure we can observe that,
The number of coupons sold by 3 Volunteers = 3 × (The number of coupons sold by each volunteer)
= 3 × 8
= 24 coupons
Hence, from the above We can conclude that,
3 volunteers sold 8 coupons each.
8 × 3 = 24 coupons sold.

Question 5.
volunteers sold 9 coupons each. × = coupons sold
Answer:
18 coupons sold.

Explanation:
It is given that, A group of volunteers was selling coupons to raise money for a food pantry.
The dot plot shows the number of coupons sold by each volunteer. Each dot represents 1 volunteer.
Now, The given figure is:

From the given figure we can observe that,
The number of coupons sold by 2 Volunteers = 2 × (The number of coupons sold by each volunteer)
= 2 × 9
= 18 coupons
Hence, from the above we can conclude that,
2 volunteers sold 9 coupons each.
2 × 9 = 18 coupons sold.

Question 6.
volunteers sold 10 coupons each. × = coupons sold
Answer:
30 coupons sold.

Explanation:
It is given that, A group of volunteers was selling coupons to raise money for a food pantry.
The dot plot shows the number of coupons sold by each volunteer.
Each dot represents 1 volunteer.
Now, The given figure is:

From the given figure we can observe that,
The number of coupons sold by 3 Volunteers = 10 × (The number of coupons sold by each volunteer)
= 10 × 3
= 30 coupons
Hence, from the above we can conclude that,
3 volunteers sold 10 coupons each.
10 × 3 = 30 coupons sold.

Question 7.
coupons were sold altogether.
Answer:
72 coupons.

Explanation:
From Questions 4, 5, and 6,
We can observe that, the total number of coupons sold 24 + 18 + 30 = 72 coupons
Hence, from the above we can conclude that,
72 coupons were sold altogether.

Question 8.
There were _____ volunteers altogether.
Answer:
8 volunteers.

Explanation:
The given figure is:

From the given figure we can observe that,
Each dot represents 1 volunteer
So, The total number of volunteers = 3 + 2 + 3 = 8 volunteers
Hence, from the above we can conclude that,
There were 8 volunteers altogether.

Question 9.
The mean number of coupons sold by the group of volunteers was _____.
Answer:
9 coupons.

Explanation:
The given figure is:

The mean number of coupons sold by the group of volunteers = \(\frac{\text {The total number of coupons sold altogether}}{\text {The total number of volunteers}}\)
= \(\frac{72}{8}\)
= 9
Hence, from the above we can conclude that,
The mean number of coupons sold by the group of volunteers was 9 coupons.

Solve.

Question 10.
Jay’s mean score for four quizzes is 8. His scores for the first three quizzes are 7.5, 8, and 9. What is Jay’s score for the last quiz?
Total score for the four quizzes = mean score × number of quizzes
= ×
=
Total score for the first three quizzes = + +
=
– =
Jay’s score for the last quiz is ______.
Answer:
Jay’s score for the last quiz is 7.5.

Explanation:
It is given that, Jay’s mean score for four quizzes is 8.
His scores for the first three quizzes are 7.5, 8, and 9.
Now we know that,
The total score for the four quizzes = (The mean of the four quizzes) × (The total number of quizzes)
So, The total score for the four quizzes 8 × 4 = 32
The total score for the first three quizzes 7.5 + 8 + 9 = 24.5
So, Jay’s score for the last quiz,
(The total score for the four quizzes) – (The total score for the first three quizzes)
= 32 – 24.5
= 7.5
Hence, from the above we can conclude that,
Jay’s score for the final quiz is 7.5

Question 11.
Sarah’s mean number of points scored for four video games is 7,500. How many points must she score in the fifth video game so that her mean score becomes 7,700?
Answer:
8,500 points.

Explanation:
It is given that, Sarah’s mean number of points scored for four video games is 7,500 and her mean score is 7,700.
We know that,
The total number of points scored by Sarah = (The mean score of Sarah) × (The total number of video games played by Sarah)
The total number of points scored by Sarah = 7,700 × 5
= 38,500 points.
The total number of points scored by Sarah in her four video games = (The mean score of Sarah) ×4
The total number of points scored by Sarah in her four video games = 7,500 × 4
= 30,000 points.
The number of points scored by Sarah in the fifth video game = (The total number of points scored by Sarah) – (The number of points scored by Sarah in her four video games)
= 38,500 – 30,000
= 8,500 points
Hence, from the above we can conclude that,
The number of points scored by Sarah in her fifth video game is 8,500 points.

Hands-On Activity

Finding Mean and Using Mean to Solve Problems

Materials

• centimeter ruler
• blank table

Work in groups of five.

Step 1: Use a centimeter ruler to measure the length of each group member’s hand to the nearest tenth of a centimeter. Record your answers in a copy of the table below.

Step 2: Use your data to answer the following questions.
What is the longest hand length?
What is the shortest hand length?
The mean hand length of the group is _____ centimeters.

Step 3: Math Journal Suppose a new student joins your group and the mean of the hand length of your group increases by 0.3 centimeters. Find the hand length of the new student to the nearest centimeter. Explain how you found your answer.
Answer:

the longest hand length is 15.4 cm
the shortest hand length is 14.9 cm
The mean hand length of the group is 15.14 centimeters.
The hand length of the new student to the nearest centimeter is 17cm.
Explanation:
First by using the ruler find the hand of the students in the class randomly in centimeters.
Then find the longest and shortest hand length from the observations recorded as shown above.
Mean = \(\frac{\text {The sum of the values}}{\text {The number of values}}\)
= \(\frac{(15.4 + 14.9 + 15.1 + 15.3 + 15.0)}{5}\)
= \(\frac{75.7}{5}\)
= 15.14 cm.
If a new student joins the group and the mean of hand length of the group increases by 0.3 cm. Then, the hand length of the new student,
Mean = 15.14 + 0.3 = 15.44 cm
15.44 = \(\frac{(15.4 + 14.9 + 15.1 + 15.3 + 15.0 + x)}{6}\)
= \(\frac{75.7x}{6}\)
x = 15.44 x 6 – 75.7
x = 92.64 – 75.7
x = 16.94
So, the hand length of the new student to the nearest centimeter is 17 cm.

Math in Focus Course 1B Practice 14.1 Answer Key

Find the mean of each data set.

Question 1.
8, 7, 5, 9, 6, 13
Answer:
8

Explanation:
The given data set is:
8, 7, 5, 9, 6, 13
We know that,
Mean = \(\frac{\text {The sum of the total data set}}{\text {The number of digits present in the data set}}\)
The mean of the given data set = \(\frac{8 + 7 + 5 + 9 + 6 + 13}{6}\)
= \(\frac{48}{6}\)
= 8
Hence, from the above we can conclude that,
The mean of the given data set is 8.

Question 2.
72 L, 91 L, 65 L, 81 L, 62 L, 83 L, 75 L, 88 L
Answer:
77.125 L

Explanation:
The given data set is:
72 L, 91 L, 65 L, 81 L, 62 L, 83 L, 75 L, 88 L
We know that,
Mean = \(\frac{\text {The sum of the total data set}}{\text {The number of digits present in the data set}}\)
The mean of the given data set = \(\frac{72 + 91 + 65 + 81 + 62 + 83 + 75 + 88}{8}\)
= \(\frac{617}{8}\)
= 77.125
Hence, from the above we can conclude that,
The mean of the given data set is 77.125 L

Question 3.
21.5 cm, 63.7 cm, 18.9 cm, 34.1 cm, 75.6 cm
Answer:
42.76 cm.

Explanation:
The given data set is:
21.5 cm, 63.7 cm, 18.9 cm, 34.1 cm, 75.6 cm
We know that,
Mean = \(\frac{\text {The sum of the total data set}}{\text {The number of digits present in the data set}}\)
The mean of the given data set = \(\frac{21.5 + 63.7 + 18.9 + 34.1 + 75.6}{5}\)
= \(\frac{213.8}{5}\)
= 42.76
Hence, from the above we can conclude that,
The mean of the given data set is 42.76 cm.

Solve. Show your work.

Question 4.
The number of goals scored by seven forwards in one soccer season was 8, 6, 4, 8, 3, 1, and 5. Find the mean number of goals scored by the seven forwards.
Answer:
5 goals.

Explanation:
It is given that,
The number of goals scored by seven forwards in one soccer season was 8, 6, 4, 8, 3, 1, and 5
We know that,
The mean number of goals scored by the seven forwards = \(\frac{\text {The total sum of the goals scored by seven forwards}}{\text {The number of goals}}\)
The mean number of goals scored by the seven forwards = \(\frac{8 + 6 + 4 + 8 + 3 + 1 + 5}{7}\)
= \(\frac{35}{7}\)
= 5
Hence, from the above we can conclude that,
The mean number of goals scored by the seven forwards is 5 goals.

Question 5.
The lengths of the five ropes are 3.2 meters, 5.2 meters, 2.9 meters, 6.6 meters, and 4.5 meters. Find the mean length of these five ropes.
Answer:
4.48 meters.

Explanation:
It is given that,
The lengths of the five ropes are 3.2 meters, 5.2 meters, 2.9 meters, 6.6 meters, and 4.5 meters
We know that,
The mean length of the five ropes = \(\frac{\text {The total length of the five ropes}}{\text {The number of ropes}}\)
The mean length of the five ropes = \(\frac{3.2 + 5.2 + 2.9 + 6.6 + 4.5}{5}\)
= \(\frac{22.4}{5}\)
= 4.48
Hence, from the above we can conclude that,
The mean length of the five ropes is 4.48 meters.

Question 6.
The masses of six chairs are 34.5 kilograms, 42.6 kilograms, 39.8 kilograms, 40.1 kilograms, 53.4 kilograms, and 33.8 kilograms. Find their mean mass.
Answer:
40.7 kilograms.

Explanation:
It is given that,
The masses of six chairs are 34.5 kilograms, 42.6 kilograms, 39.8 kilograms, 40.1 kilograms, 53.4 kilograms, and 33.8 kilograms.
We know that,
The mean mass of the six chairs = \(\frac{\text {The total mass of the six chairs}}{\text {The number of chairs}}\)
The mean mass of the six chairs = \(\frac{34.5 + 42.6 + 39.8 + 40.1 + 53.4 + 33.8}{6}\)
= \(\frac{244.2}{6}\)
= 40.7 kilograms
Hence, from the above we can conclude that,
The mean mass of the six chairs is 40.7 kilograms.

Use the data in the table to answer the question.

The table shows a sprinter’s times for the 100-meter dash at the first five meets of one season.

Question 7.
What was the sprinter’s meantime for the 100-meter dash at these meets?
Answer:
10.116 s

Explanation:
It is given that,
The table shows a sprinter’s times for the 100-meter dash at the first five meets of one season.
The given table is:

From the above table we can observe that,
The sprinter’s meantime for the 100-meter dash at these meets = \(\frac{\text {The total time taken to complete the 100-meter dash}}{\text {The number of meets}}\)
The sprinter’s meantime for the 100-meter dash at these meets = \(\frac{10.09 + 10.14 + 10.29 + 10.07 + 9.99}{5}\)
= \(\frac{50.58}{5}\)
= 10.116 s
Hence, from the above we can conclude that,
The sprinter’s meantime for the 100-meter dash at these meets is 10.116 s.

Use the data in the dot plot to answer questions 8 and 9

Eight ice hockey teams competed in the quarter-finals of a national championship. The dot plot on the right shows the number of goals scored by each team. Each dot represents 1 team.

Question 8.
What was the total number of goals scored by the eight teams?
Answer:
26 goals.

Explanation:
It is given that,
Eight ice hockey teams competed in the quarter-finals of a national championship.
The dot plot shows the number of goals scored by each team.
Each dot represents 1 team.
The given figure is:

From the given figure we can observe that,
The total number of goals scored by the eight teams = (The total number of teams) × (The total number of goals made by each team)
= (2 × 2) + (3 × 3) + (4 × 2) + (5 × 1)
= 4 + 9 + 8 + 5
= 26 goals
Hence, from the above we can conclude that,
The total number of goals scored by the eight teams is 26 goals.

Question 9.
What was the mean number of goals scored by each team?
Answer:
3 goals.

Explanation:
From Question 8,
We can observe that the total number of goals scored by the eight teams is 26 goals.
We know that the mean number of goals scored by each team,
\(\frac{\text {The total number of goals scored by the eight teams}}{\text {The total number of teams}}\)
The mean number of goals scored by each team = \(\frac{26}{8}\)
= 3.25
≅ 3 goals
Hence, from the above we can conclude that,
The mean number of goals scored by each team is about 3 goals.

Solve. Show your work.

Question 10.
The mean of the five numbers 3, 7, 9, 12, and x is 8. Find the value of x.
Answer:
x = 9

Explanation:
It is given that the mean of the five numbers 3, 7, 9, 12, and x is 8
We know that,
Mean = \(\frac{\text {The sum of the numbers}}{\text {The count of the numbers}}\)
The mean of the five numbers = \(\frac{3 + 7 + 9 + 12 + x}{5}\)
8 = \(\frac{31 + x}{5}\)
31 + x = 8 × 5
x = 40 – 31
x = 9
Hence, the value of x is 9.

Question 11.
The mean of a set of five numbers is 4.8. Given that the sixth number is x and the mean of these six numbers is 5.5, find the value of x.
Answer:
x = 9

Explanation:
It is given that the mean of a set of five numbers is 4.8.
Mean = \(\frac{\text {The sum of the numbers}}{\text {The count of the numbers}}\)
The total sum of the set of five numbers = 4.8 × 5
= 24
The total sum of the set of six numbers 5.5 × 6 = 33
The value of the sixth number (x) = (The total sum of the set of six numbers) – (The total sum of the set of five numbers)
= 33 – 24
= 9
Hence, the value of x is 9.

Question 12.
In a race, the meantime for three runners was 12.4 seconds and the meantime for another six runners was 11.5 seconds. Calculate the meantime for all the nine runners.
Answer:
23.9 seconds.

Explanation:
It is given that, in a race, the meantime for three runners was 12.4 seconds and the meantime for another six runners was 11.5 seconds.
The meantime for all the nine runners = (The meantime for three runners) + (The meantime for six runners)
The meantime for all the nine runners = 12.4 + 11.5
= 23.9 seconds
Hence, the meantime for all the nine runners is 23.9 seconds.

Question 13.
The mean weight of nine apples is 7.5 ounces. Three of the apples have a mean weight of 8 ounces. Find the mean weight of the other six apples.

Answer:
7.25 ounces.

Explanation:
It is given that the mean weight of nine apples is 7.5 ounces.
Three of the apples have a mean weight of 8 ounces
We know that,
The total mean weight of nine apples = (The total mean weight of three apples) + (The total mean weight of six apples)
So, The total weight of six apples = (The total weight of nine apples) – (The total weight of three apples)
= (7.5 × 9) – (8 × 3)
= 67.5 – 24
= 43.5 ounces
The total mean weight of six apples = \(\frac{\text {The total weight of six apples}}{\text {The number of apples}}\)
= \(\frac{43.5}{6}\)
= 7.25 ounces
Hence, the mean weight of the other six apples is 7.25 ounces.

Question 14.
The mean of six numbers is 45. Four of the numbers are 40, 38, 46, and 51. If the remaining two numbers are in the ratio 2 : 3, find the two numbers.
Answer:
38 and 57 are the numbers.

Explanation:
It is given that the mean of six numbers is 45.
Four of the numbers are 40, 38, 46, and 51 and the remaining two numbers are in the ratio 2 : 3
Now, Let
x—–> the missing smaller number
y—-> the missing larger number
We know that,
Mean = \(\frac{\text {The sum of the numbers in the data set}}{\text {The number of values present in the data set}}\)
45 = \(\frac{40 + 35 + 46 + 51 + x + y}{6}\)
40 + 35 + 46 + 51 + x + y = 270
175 + x + y = 270
x + y = 95  —–> Equation A
It is also given that, \(\frac{x}{y}\) = \(\frac{2}{3}\)
x = \(\frac{2}{3}\)y  —–> equation B
Now, substitute equation B in equation A and solve for y.
So, \(\frac{2}{3}\)y + y = 95
y (1 + \(\frac{2}{3}\) ) = 95
\(\frac{5}{3}\)y = 95
y = 95 × \(\frac{3}{5}\)
y = 19 × 3
y = 57
Now, substitute the value of y in Equation B.
So, x = \(\frac{2}{3}\) × 57
x = 2 × 19
x = 38
Hence, the two numbers are 38 and 57.

Question 15.
A data set consists of three numbers, a, b, and c. Write an algebraic expression, in terms of a, b, and c, to represent the mean of the new set of numbers obtained by
a) adding 5 to every number in the set.
Answer:
\(\frac{a + b + c}{3}\) + 5

Explanation:
It is given that a data set consists of three numbers, a, b, and c
We know that,
Mean = \(\frac{\text {The sum of the numbers in the data set}}{\text {The number of values present in the data set}}\)
According to the given condition,
We have to add 5 to each value
So, The sum of the numbers = (a + 5) + (b + 5) + (c + 5)
= (a + b + c) + 15
So, The mean of the new set of numbers = \(\frac{(a + b + c) + 15}{3}\)
= \(\frac{a + b + c}{3}\) + 5
Hence, the mean of the new set of numbers is \(\frac{a + b + c}{3}\) + 5

b) doubling every number in the set.
Answer:
\(\frac{2}{3}\) (a + b + c)

Explanation:
Given that a data set consists of three numbers, a, b, and c.
We know that,
Mean = \(\frac{\text {The sum of the numbers in the data set}}{\text {The number of values present in the data set}}\)
According to the given condition,
We have to double each value i.e., we have to multiply each value with 2
So, The sum of the numbers = (a + a) + (b + b) + (c + c)
= 2a + 2b + 2c
= 2(a + b + c)
So, The mean of the new set of numbers = \(\frac{2(a + b + c)}{3}\)
= \(\frac{2}{3}\) (a + b + c)
Hence, the mean of the new set of numbers is \(\frac{2}{3}\) (a + b + c)

c) halving every number in the set.
Answer:
\(\frac{1}{6}\) (a + b + c)

Explanation:
Given that, A data set consists of three numbers, a, b, and c.
We know that,
Mean = \(\frac{\text {The sum of the numbers in the data set}}{\text {The number of values present in the data set}}\)
According to the given condition,
We have to half each value i.e., we have to multiply each value with 0.5 or \(\frac{1}{2}\)
So, The sum of the numbers = (a × 0.5) + (b × 0.5) + (c × 0.5)
= 0.5a + 0.5b + 0.5c
= 0.5(a + b + c)
So, The mean of the new set of numbers = \(\frac{0.5(a + b + c)}{3}\)
= \(\frac{0.5}{3}\) (a + b + c)
= \(\frac{1}{6}\) (a + b + c)
Hence, the mean of the new set of numbers is \(\frac{1}{6}\) (a + b + c)

Question 16.
The table shows the mean scores of three classes in a history test.

The mean score of all the students in classes A and B combined is 6.8
The mean score of all the students in classes B and C combined is 7.
If the number of students in classes A, B, and C are denoted by a, b, and c respectively, find the ratio a: b: c.

Answer:
a : b : c = 4 : 6 : 3

Explanation:
Let number of students in A = a
Let number of students in B = b
Let number of students in C = c

Total score of A ÷ a = 8
Total score of A = 8 x a = 8a

Total score of B ÷ b = 6
Total score of B = 6 x b = 6b

Total score of C ÷ c = 9
Total score of C = 9 x c = 9c

Total score of (A + B) ÷ (a + b) = 6.8
Total score of (A + B) = 6.8 x (a + b) = 6.8a + 6.8b
Total score of A + Total score of B = 6.8a + 6.8b
8a + 6b = 6.8a + 6.8b
1.2a = 0.8b
3a = 2b
a : b = 2 : 3

Total score of (B + C) ÷ (b + c) = 7
Total score of (B + C) = 7 x (b + c) = 7b + 7c
Total score of B + Total score of C = 7b + 7c
6b + 9c = 7b + 7c
b = 2c
b : c = 2 : 1

now we have
[a : b = 2 : 3] x 2
[b : c = 2 : 1] x 3

a : b = 4 : 6
b : c = 6 : 3

a : b : c = 4 : 6 : 3

Question 17.
Math Journal Find five different numbers whose mean is 12. Explain your strategy.
Answer:
Answers may vary.
The five different numbers whose mean is 12 are 10, 11, 12, 13 and14.

Explanation:
The mean is the average of the numbers.
Add up all the numbers, then divide by how many numbers there are.
10 + 11 + 12 + 13 + 14 = 65
So, divide the sum by the count or number of terms.
65 ÷ 5 = 12

Go through the Math in Focus Grade K Workbook Answer Key Chapter 3 Order by Size, Length, or Weight to finish your assignments.

Math in Focus Kindergarten Chapter 3 Answer Key Order by Size, Length, or Weight

Lesson 1 Ordering Things by Size

Look and talk

Answer:

Explanation:
Ordering the things according to Bath Robes and Pillow sizes
1. Papa Bear’s,
2. Mama Bear’s and finally
3. Baby Bear’s.

Answer:

Explanation:
Ordering the things according to Combs, Brushes and Slippers sizes
1. Papa Bear’s,
2. Mama Bear’s and finally
3. Baby Bear’s.

Which is the biggest? Color. Which is the smallest? Circle.

Question 1.

Answer:

Explanation:
Colored the biggest one and circled the smallest sock.

Question 2.

Answer:

Explanation:
Colored the biggest one and circled the smallest hat.

Question 3

Answer:

Explanation:
Colored the biggest one and circled the smallest shirt.

Lesson 2 Comparing Sizes

Draw.

Question 1.

Answer:

Explanation:
Drawn bigger ball than the given ball.

Question 2.

Answer:

Explanation:
Drawn the smaller flower than the given flower.
Question 3.

Answer:

Explanation:
Drawn the taller boy than the given boy.

Question 4.

Answer:

Explanation:
Drawn the trouser which is shorter than the given trouser.

Lesson 3 Ordering Things by Length

Color the longest snake yellow. Color the shortest snake red.

Answer:

Explanation:
Colored the longest snake yellow and Colored the shortest snake red above.

Lesson 4 Ordering Things by Weight

Which is the heaviest? Circle.

Question 1.

Answer:

Explanation:
Circled the heaviest one.

Question 2.

Answer:

Explanation:
Circled the heaviest one.

Question 3.

Answer:

Explanation:
Circled the heaviest one.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 7 Solid and Flat Shapes to finish your assignments.

Math in Focus Kindergarten Chapter 7 Answer Key Solid and Flat Shapes

Lesson 1 Solid Shapes

Which shape is it? Color.

Question 1.

Answer:

Explanation:
Cone Shape,
Colored Icecream, Cap, Announcement Speaker.

Question 2.

Answer:

Explanation:
Circle shape – Balls, Bubbles,
Cone shape – Caps, Lamp.

Lesson 2 Flat Shapes in Solid Shapes

Match

Answer:

Explanation:
Matched with the given solid shapes,
Cube- Square,
Rectangle – Game Puzzel.

Answer:

Explanation:
Matched with the given solid shape
Round-Circle- Balloons, Ball,
Triangle –  Prism.

Pair

Answer:

Explanation:
Circle – Sun,
Rectangle – Tissue Box,
Triangle – Prism,
Sqaure – Clock.

Lesson 3 Flat Shapes

Draw

Question 1.

Answer:

Explanation:
Drawn Big Circle and Small Circle in the given space.

Question 2.

Answer:

Explanation:
Drawn Small Sqaure and Big Square in the given place.

Question 3.

Answer:

Explanation:
Drawn Big Triangle and Small Triangle in the given space.

Question 4.

Answer:

Explanation:
Drawn Small Rectangle and Big Rectangle in the given space.

Question 5.

Answer:

Explanation:
Drawn Big Hexagon and Small Hexagon in the given space.

Lesson 4 Flat Shape Pictures

Color the squares red. Color the rectangles green. Color the circle yellow.
Color the triangle blue. Color the hexagon brown.

Answer:

Explanation:
Colored the squares with red. Colored the rectangles with green.
Colored the circles with yellow.
Colored the triangles with blue. Colored the hexagons with brown.

Lesson 5 Shape Patterns

Complete the pattern.

Question 1.

Answer:

Explanation:
Completed the given pattern in the given box.

Question 2.

Answer:

Explanation:
Completed the given pattern in the given box.

Question 3.

Answer:

Explanation:
Completed the given pattern in the given box.