COAL B
Notes on Two-Way Frequencies
Name _____________________________
Warm Up
The table to the right is called a frequency table. It shows the frequency each data value occurs. The
data of this table is divided into intervals.
1. How many children were between the ages of 4 and 5?
2. How many children were between the ages of 6 and 9?
3. How many total children were sampled?
--------------------------------------------------------------------------------------------------------------------Two-Way Tables
A two-way table is a useful way to organize data that can be categorized by two variables. Suppose you
asked 20 children and adults whether they liked broccoli. The table shows one way to arrange the data.
1. How many Children were surveyed?
2. How many who were surveyed answered yes?
3. How many Adults answered no?
---------------------------------------------------------------------------------------------------------------------
Students were surveyed about their favorite subject.
1. How many 9th Grade students were surveyed?
2. How many students answered Math?
3. How many 11th Graders answered English?
4. How many total students were surveyed?
--------------------------------------------------------------------------------------------------------------------Table shows the results of 125 randomly selected individuals of those surveyed:
1. How many Adults were surveyed?
2. How many had at least 1 accident?
3. How many teens had one or more accidents?
--------------------------------------------------------------------------------------------------------------------The joint relative frequencies are the values in each category divided by the total number of values.
Divide each value by 20 (the total number of individuals)
Find the Joint Relative Frequencies of the following:
--------------------------------------------------------------------------------------------------------------------Find the Joint Relative Frequencies of the table below:
--------------------------------------------------------------------------------------------------------------------Marginal Relative Frequencies:The marginal relative frequencies are found by adding the joint relative
frequencies in each row and column.
--------------------------------------------------------------------------------------------------------------------The table shows the number of books sold at a library sale. Complete the table with the joint and
marginal relative frequencies.
--------------------------------------------------------------------------------------------------------------------Classwork/Homework
1. The ______________________ relative frequencies are the sums of each row and column in a twoway table.
2. The table shows the results of a poll of randomly selected high school students who were asked if
they prefer to hear all-school announcements in the morning or afternoon. Make a table of the joint
and marginal relative frequencies.
Under
Underclassmen Upperclassmen
Morning
8
Afternoon 18
14
Morning
10
Afternoon
Total
Upper
Total
Classwork/Homework Continued
Name _________________________
3. The table shows the results of a customer satisfaction survey for a cellular service provider,
by location of the customer. In the survey, customers were asked whether they would
recommend a plan with the provider to a friend.
Make a table of the joint and marginal relative frequencies. Round to the nearest hundredth
where appropriate.
Arlington Towson
Arlington Towson
Parkville
Yes
40
35
41
Yes
No
18
10
6
No
Parkville
Total
Total
Classwork/Homework Continued
Name _________________________
3. The table shows the results of a customer satisfaction survey for a cellular service provider,
by location of the customer. In the survey, customers were asked whether they would
recommend a plan with the provider to a friend.
Make a table of the joint and marginal relative frequencies. Round to the nearest hundredth
where appropriate.
Arlington Towson
Parkville Total
Arlington Towson Parkville
Yes
40
35
41
Yes
No
18
10
6
No
Total
Classwork/Homework Continued
Name _________________________
3. The table shows the results of a customer satisfaction survey for a cellular service provider,
by location of the customer. In the survey, customers were asked whether they would
recommend a plan with the provider to a friend.
Make a table of the joint and marginal relative frequencies. Round to the nearest hundredth
where appropriate.
Arlington Towson
Parkville Total
Arlington Towson Parkville
Yes
40
35
41
Yes
No
18
10
6
No
Total