Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables

We included HMH Into Math Grade 8 Answer Key PDF Module 9 Lesson 1 Construct and Interpret Two-Way Frequency Tables to make students experts in learning maths.

HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables

I Can construct a two-way table summarizing data, complete a table given partial data, and interpret data to determine whether there is an association between two variables.

Spark Your Learning

A technology company conducts a survey to find out how many people have a selfie stick and how many have a photo-editing app on their phone. The table shows the results of the survey.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 1
What can you determine from the data in the table?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 2
Answer:
Has app with selfie stick – 51 and no selfie stick – 26,
Non app with selfie stick – 31 and no selfie stick – 42,

Explanation:
Given a technology company conducts a survey to find out how many people have a selfie stick and
Number of many have a photo-editing app on their phone.
The table shows the results of the survey from the data in the given table I can detrmine that number of people has app with selfie stick are 51 and app with no selfie stick are 26,
Those with non app with selfie stick are 31 and without no selfie stick – 42,

Turn and Talk Does there seem to be any relationship between owning a selfie stick and having a photo editing app? Explain.
Answer:
No relationship,

Explanation:
There seem to be no relationship between owning a selfie stick and having a photo editing app because without selfie stick we can take photo but without photo editing app we cannot edit our photos.

Build Understanding

Connect to Vocabulary
You have already used tables to look for patterns in data. A two-way table is a table that displays two-variable data by organizing it into rows and columns.

Question 1.
A software company gives its employees the choice of using a treadmill desk or a regular desk. Employees can also choose a laptop computer or a tablet computer. The two-way table shows the results from a survey of 200 company employees.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 3
A. Explain how you can fill in the missing value in the bottom row of the table. Then fill in the value.
Answer:
200 – 34 = 166,

Explanation:
By subtracting Treadmill total from overall total I can find the missing value in the bottom row of the table. Then fill in the value as 200 – 34 = 166.

B. Explain how you can fill in the missing values in the “Treadmill desk” column and “Regular desk” column. Then fill in the values.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 4
Answer:
Treadmill desk : Laptop : 34 – 20 = 14,
Regular desk : Tablet : 166 – 79 = 87,

Explanation:
The missing values in the “Treadmill desk” column are as it is already given “Treadmill desk” total 34 and Tablet 20 so Treadmill desk : Laptop : 34 – 20 = 14 and we got Regular desk total as 166 and
Regular desk : Laptop : 79, so Regular desk : Tablet : 166 – 79 = 87.

C. Explain how you can fill in the missing values in the “TOTAL” column on the right side of the table. Then fill in the values.
Answer:
TOTAL Laptop : 93,
TOTAL Tablet : 107,

Explanation:
The missing values in the “TOTAL” column on the right side of the table.
TOTAL Laptop : Treadmill desk : Laptop + Regular desk : Laptop = 14 + 79 = 93,
TOTAL Tablet : Treadmill desk : Tablet + Regular desk : Tablet = 20 + 87 = 107.

D. Explain how you can check that the values you wrote in the “TOTAL” column are correct.
Answer:
Checking with TOTAL 200,

Explanation:
To check that the values that I wrote in the “TOTAL” column are correct are by adding TOTAL Laptop + TOTAL Tablet = 93 + 107 = 200 and checking with TOTAL 200, we get same values therefore it is correct.

Turn and Talk Is there a different sequence of steps you can use to fill in the two-way table? Explain.
Answer:
Finding Treadmill desk : Laptop : 14,
TOTAL Laptop : 93,
TOTAL Tablet = TOTAL – TOTAL Laptop = 200 – 93 = 107,
TOTAL Regular desk : 87,
TOTAL check = TOTAL Treadmill desk + TOTAL Regular desk =
34 + 166 = 200,

Explanation:
Different sequence of steps I can use to fill in the two-way table are
1. Treadmill desk : Laptop : 34 – 20 = 14,
2. TOTAL Laptop : Treadmill desk : Laptop + Regular desk : Laptop =
14 + 79 = 93,
3. TOTAL Tablet = TOTAL – TOTAL Laptop = 200 – 93 = 107,
4. TOTAL Regular desk : Tablet = TOTAL Tablet – Total Treadmill desk = 107 – 20 = 87, Checking with TOTAL 200 as TOTAL check = TOTAL Treadmill desk + TOTAL Regular desk = 34 + 166 = 200 which is correct.

Step It Out

Question 2.
A survey asked 80 adults about gym memberships and exercise apps. Of those without a gym membership, 16 had an exercise app on their phone. Construct a two-way frequency table to display the data.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 5
A. Fill in the given information: the TOTAL number of adults in the bottom right cell, the 48 TOTAL adults with a membership, the 16 adults without a membership and with an exercise app, and the 36 adults with both a membership and an exercise app.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 6
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-1

Explanation:
Given to fill the given information: the TOTAL number of adults in the bottom right cell,
the 48 TOTAL adults with a membership, the 16 adults without a membership and with an
exercise app, and the 36 adults with both a membership and an exercise app filled as shown above,
Has membership and has app as 36, 48 TOTAL adults with a membership, So no app but has membership is 48 -36 = 12, 16 adults without a membership and with an exercise app, No app no membership is 28 – 12 = 16, TOTAL no membership 80 – 48 = 32, Filled all the data as shown above in the table.

Connect to Vocabulary
To determine if there is an association between two categories, divide the number of people who fit into both categories by the total for one of those categories. If that percentage is greater than the percentage of all people surveyed who are in that one category, then the categories have an association.

B. Complete the TOTAL column: you know that 48 of the 80 adults surveyed have a gym members.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7 = _____________ adults do not have a membership
Answer:
80 – 48 = 32,
32 adults do not have a membership,

Explanation:
Completed the TOTAL column:
As I know that 48 of the 80 adults surveyed have a gym members, So 80 – 48 = 32, therefore 32 adults do not have a membership.

C. Now fill in the top row. Use the fact that 36 of those with a gym membership have an exercise app on their phone.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7 = _____________ adults with a membership have no app
Answer:
48 – 36 = 12,
12 adults with a membership have no app,

Explanation:
Now filling in the top row. Using the fact that 36 of those with a gym membership have an exercise app on their phone as 48 – 36 = 12, 12 adults with a membership have no app.

D. Next, fill in the second row.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 7 = _____________ adults without a membership have no app on their phone
Answer:
28 – 12 = 16,
16 adults without a membership have no app on their phone,

Explanation:
No app no membership is 28 – 12 = 16 therefore 16 adults without a membership have no app on their phone.

E. Finally, in each column, add the values in the top two rows to get the value for the TOTAL cell in the bottom row.
Answer:
TOTAL Has app 36 + 16 = 52,
TOTAL No app 12 + 16 = 28,

Explanation:
Finally, in each column, added the values in the top two rows to get the value for the TOTAL cell
in the bottom row as TOTAL has app = Has App : Has membership + Has App : Has no member ship = 36 + 16 = 52, TOTAL No app = No app : Has membership + No App : Has no membership =
12 + 16 = 28.

F. What percentage of the adults surveyed have an exercise app?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 8
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-2
Explanation:
The percentage of the adults surveyed have an exercise app is
Total number of adults with app /  Total number of adults surveyed =
52/80 = 0.65 = 65%.

G. What percentage of the adults surveyed who have a gym member have an exercise app?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 9
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-3

Explanation:
The percentage of the adults surveyed who have a gym member have an exercise app is
Number of adults with gym membership and app/ Total number with gym membership = 36/48 = 0.75 = 75%.

H. Is there an association between having a gym membership and having an exercise app? Explain.
Answer:
Yes,
We can know number of adults with Has membership: No app,

Explanation:
Yes, There is an association between having a gym membership and having an exercise app,
we can know from the number of adults with Has membership : No app andwith TOTAL : Has membership minus gym membership and having an exercise app as 48 – 36 = 12 adults.

Question 3.
At a school, 120 students were asked whether they take the subway to school. They were also asked whether they arrived late to school in the past week. The two-way table shows the results. Is there an association between taking the subway and arriving late to school?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 10
A. Find the percentage of all students who arrived late at school.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 11
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-4

Explanation:
Given to find the percentage of all students who arrived late at school is Total number of students who arrived late/ Total number of students surveyed = 18/120 = 0.15 = 15%.

B. Find the percentage of students who arrived late among those who took the subway.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 12
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-5

Explanation:
The percentage of students who arrived late among those who took the subway are Number of students who took subway and arrived late/ Total number of students who too subway =
12/30 = 0.4 = 40%.

C. Students who took the subway to school were (more / less) likely to arrive late than the general population of students. There (is / is not) an association between taking the subway and arriving late.
Answer:
less,
is,

Explanation:
Students who took the subway to school were less likely to arrive late than the general population of students. There is an association between taking the subway and arriving late.
12 students are taking the subway and arriving late.

Check Understanding

Question 1.
Customers at a sporting goods store were surveyed.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 13
A. Complete the table.
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-6

Explanation:
Completed the table as shown above.

B. How many customers were surveyed?
Answer:
500,

Explanation:
Total 500 customers were surveyed.

C. Is there an association between watching and playing soccer? Explain.
Answer:
Yes,

Explanation:
Yes there an association between watching and playing soccer as out of 500 customers 144 customers
watch and play soccer.

On Your Own

Question 2.
In a survey of 160 people who have reptiles as pets, 40% have a pet snake. Of those with a pet snake, 25% also have a pet lizard. Of those who do not have a pet snake, 75% have a pet lizard.
A. Construct a two-way frequency table to display the data.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 14
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-8

Explanation:
Constructed a two-way frequency table to display the data of survey of 160 people who have reptiles as pets, 40% have a pet snake. Of those with a pet snake, 25% also have a pet lizard. Of those who do not have a pet snake, 75% have a pet lizard as shown above.

B. What percentage of those surveyed have a pet lizard?
Answer:
100%,

Explanation:
The percentage of those surveyed have a pet lizard is Total number of has lizards/ Total number of surveyed people X 100 = 160/160 X 100 = 100%.

C. What percentage of those surveyed have both a snake and a lizard?
Answer:
25%,

Explanation:
The percentage of those surveyed have both a snake and a lizard is percentage of those surveyed have both a snake and a lizard/ Total number of surveyed people X 100 = 40/160 X 100 = 25%.

Question 3.
Reason A park ranger surveyed 300 visitors to a national park as they arrived. She asked the visitors whether they planned to camp in the park and whether they planned to hike in the park. The two-way table shows the results.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 15
Is there an association between camping in the park and hiking in the park? Explain.
Answer:
Yes,

Explanation:
Yes there is association between camping in the park and hiking in the park as 135 visitors are associated with camping and hiking in the park.

Question 4.
STEM Scientists often use two-way frequency tables to determine the effectiveness of a treatment. Suppose scientists want to know whether a new herbal tea helps reduce headaches. They may ask a group of people to drink the tea for a week and record whether or not they get a headache.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 16
Based on the results in the two-way frequency table, can the scientists conclude that the herbal tea helps reduce headaches? Explain.
Answer:
No, scientists will not conclude that herbal tea will reduce total headaches,

Explanation:
Given results in the two-way frquency table, Scientists can conclude that the herbal tea will not help
to reduce headaches as out of 210 people with tea only 84 people have no headaches means 35% only, therefore scientists will not conclude that herbal tea will reduce total headaches.

Question 5.
Open-Ended Conduct a survey of students in your class. Each student that you survey should be asked whether or not the student has a curfew on school nights and whether or not the student has assigned chores at home. Record your survey data in the table.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 17
Is there evidence of an association between having a curfew on school nights and having chores? Explain.
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-9
Yes there is an association between having a curfew on school nights and having chores,

Explanation:
Conducting a survey of 100 students in my class. Each student that you survey should be asked whether or not the student has a curfew on school nights and whether or not the student has assigned chores at home.
Recorded my survey data in the table as 12 students curfew with chores, 34 students with curfew no chores, 40 are no curfew with chores and 14 are no curfew and no chores above. Yes there is an association between having a curfew on school nights and having chores as 12 students are associated.

I’m in a Learning Mindset!

How did the decisions I made constructing two-way frequency tables support my learning and that of others in my class?
Answer:
The over all total is correct and matched,

Explanation:
The decisions I made constructing two-way frequency tables support my learning and that of others in my class by checking the data of with curfew and chores, curfew and no chores,
No curfew and chores and lastly with no curfew and no chores total has matched with all the data.

Lesson 9.1 More Practice/Homework

Question 1.
Attend to Precision In a survey of 200 people who visited China, 85% visited the Great Wall. Of those who visited the Great Wall, 30% also visited the Chengdu Panda Center. Of those who did not visit the Great Wall, 80% visited the Panda Center. Complete the two-way frequency table.
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 18
Answer:
Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables-10
Explanation:
Attended to Precision in a survey of 200 people who visited China, 85% visited the Great Wall.
Of those who visited the Great Wall, 30% also visited the Chengdu Panda Center. Of those who did not visit the Great Wall, 80% visited the Panda Center.
Completed the two-way frequency table as
Total visited the Great Wall are 85 X 200/100 = 170 people, as of those who visited the Great Wall, 30% also visited the Chengdu Panda Center so 30 X 170/100 = 51 people,
visited the Great Wall of those who did not visit Chengdu Panda
Center 170 – 51 = 119 people,
30% also visited the Chengdu Panda Center.
Of those who did not visit the Great Wall,
80% visited the Panda Center so 15% did not visit
so 15 X 200/100 = 30 people, now out of 30 people
80% visited the Panda Center means 80 X 30/100 = 24 people,
Total did not visit Great Wall are 200 – 170 = 30 people,
Did not visit Great Wall and Did not visit
Chengdu Panda Center are 30 – 24 = 6 people respectively above.

Question 2.

Math on the Spot Determine whether there is an association between the events.
A. Thirty-two students were polled about whether they have a phone plan with texting and whether they have had an accident. Find the percentages of those having an accident for both the general population of students and for students who have a phone with texting. Is there an association between having a phone with texting and having an accident?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 19
Answer:
The percentage of those having an accident for
both the general population of students are 50%,
The percentage for students who have a phone with texting are 75%,
Yes, 16 are associated between having a phone
with texting and having an accident,

Explanation:
Given thirty-two students were polled about whether they have a phone plan with texting and whether they have had an accident.
the percentage of those having an accident for both the general population of students are 16/32 X 100 = 50%,
the percentage for students who have a phone with texting are
12/16 X 100 = 75%, Yes, 16 are associated between having a phone with texting and having an accident.

B. Middle school and high school students were polled about whether they had visited an amusement park. Find the percentages of those having visited an amusement park for both the general population of students and for high school students. Is there an association between being a high school student and visiting an amusement park?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 20
Answer:
The percentage of those having visited an amusement park for both the general population of students are 80%, The percentage of those having visited an amusement park for high school students are 75%,
Yes, Association is there between being a high school student and visiting an amusement park,

Explanation:
Given middle school and high school students were polled about whether they had visited an amusement park.
The percentage of those having visited an amusement park for both the general population of students are 80/100 X 100 = 80%. The percentage of those having visited an amusement park
for high school students are 60/80 X 100 = 75%, Yes, 60 students are associated between being a high school student and visiting an amusement park.

Test Prep

Question 3.
Keysha surveyed adults in her city. The results are shown in the table. Which of the following is a true statement?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 21
(A) More people own a bike than own a car.
(B) A total of 68 people surveyed own a bike.
(C) Of the people with a bike, 27 also have a car.
(D) There are 42 bike owners who do not own a car.
Answer:
(C) Of the people with a bike, 27 also have a car,

Explanation:
Keysha surveyed adults in her city. The results are given in the table. Based on that table the following is a true statement of the people with a bike, 27 also have a car matches with bit (C).
Upon checking all other bits (A), (B) and (D) are false.

Question 4.
A gardener tried a new spray-on some plants to see if the spray prevents aphids. The table shows the results. What is the value of x?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 22
(A) 7
(B) 10
(C) 18
(D) 28
Answer:
(B) 10,

Explanation:
Given a gardener tried a new spray-on some plants to see if the spray prevents aphids. The table showed the results. Completed the table as shown above therefore the value of x
is 10 which matches with bit (B).

Question 5.
Students at a local community college can study Spanish or French. They also have a choice of band or chorus for their music classes. The table shows the results of surveying 100 students. Which is a correct statement about students who study Spanish and students who choose band?
HMH Into Math Grade 8 Module 9 Lesson 1 Answer Key Construct and Interpret Two-Way Frequency Tables 23
(A) There is no association because students who study Spanish are no more or less likely than other students to choose band.
(B) There is no association because students who study Spanish are less likely than other students to choose band.
(C) There is an association because students who study Spanish are more likely than other students to choose band.
(D) There is an association because students who study Spanish are less likely than other students to choose band.
Answer:
(D) There is an association because students who study
Spanish are less likely than other students to choose band,

Explanation:
Given students at a local community college can study Spanish or French. They also have a choice of band or chorus for their music classes. The table showed the results of surveying 100 students. The correct statement about students who study Spanish and students who choose band as out of
64 spanish students only 16 students choose band so the statement is,
There is an association because students who study Spanish are less likely than other students to choose band which matches with bit (D).

Spiral Review

Question 6.
A chili cook-off has adult tickets a and child tickets c. A group of visitors buys 3 adult tickets and 2 child tickets and pays a total of $26. Another group buys 5 adult tickets and 3 child tickets and pays $42. Write and solve a system of equations to find the price of each type of ticket.
Answer:
Equations:
3a + 2c = 26,
5a + 3c = 42,
Price of adult ticket is $6 and child ticket is $4,

Explanation:
Given a chili cook-off has adult tickets a and child tickets c.
A group of visitors buys 3 adult tickets and 2 child tickets and
pays a total of $26. Another group buys 5 adult tickets and
3 child tickets and pays $42.
System of equations are 3a + 2c = 26 — Equation (1),
5a + 3c = 42 — Equation (2) now solving multiplying
equation (1)  by 3 and equation (2) by 2 and subtracting
equation (2) from equation(1) as
10a + 6c = 84
-9a – 6c = – 72
a + 0 = 6,
Therefore adult ticket is $6,
Now as a = $6 substituting in equation (1) we get
3 X 6 + 2c = 26,
18 + 2c = 26,
2c = 26 – 18 = 8, c = 8/2 = 4,
Therefore, price of adult ticket is $6 and child ticket is $4.

Question 7.
Without graphing, find the point of intersection of the lines -x + 2y = -4 and 2x + y = 3.
Answer:
The point of intersection is (2,-1),

Explanation:
Given to find without graphing the point of intersection of the lines -x + 2y = -4 and 2x + y = 3.
“The point of intersection” of two equations is the point (in this case in the xy-plane) where the lines
represented by the two equations intersect; because it is a point on both lines, it is a valid solution pair for both equations. In other words, it is a solution to both equations; in this case it is a solution to both: -x + 2y = -4 and 2x + y = 3. The simplest thing to do is to convert each of these
expressions into the form x = something so x = 2y + 4, and 2x + y = 3, x = (3 – y)/2,
Since both right-hand sides are equal to x, we have: 2y + 4 = (3 – y)/2, 2(2y + 4) = 3 – y,
4y + 8 = 3 – y, 4y + y = 3 – 8, 5y = – 5, y = -5/5 = -1, So x = 2(-1) + 4 = -2 + 4 = 2,
Solution is (x , y) = (2, -1) therefore the point of intersection is (2,-1).

Question 8.
The graph of a proportional relationship passes through the point (6, 21). What is the equation for the relationship?
Answer:
The equation for the relationship is y = 7/2 x or 2y = 7x,

Explanation:
Given that point (x, y) = (6,21) is part of a direct relationship,
That is: y is proportion to x, y = k X  x (1), Where k is the proportionality constant.
If we know that x= 6 and y =21 then the proportionality constant is: k = y/x,
k = 21/6, k = 7/2, Lastly, the equation for the relationship is y = 7/2 x or 2y = 7x.

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