Lesson 48
Mr. Jones
Trigonometry
Name:_______________________
Date:___________________
S.W. B. A. T: Construct a two-way frequency table. Construct a two-way table
containing the joint and marginal frequencies. Interpret a two-way frequency
table and identify the frequencies within the table (joint, marginal)
DO NOW: Suppose you randomly survey the freshmen and sophomores about whether they
are attending a school concert. Complete the following table containing the results.
Attending
25
80
Freshmen
Sophomores
Total
Not Attending
Total
69
32
Definitions
Relative frequency is the interval frequency, f, divided by the total frequency, n.
Relative frequency =
𝑓
𝑛
=
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
Two-way frequency table (also called a contingency table) is a frequency table that displays
data that belongs to two different categories. For instance, a table can show the leisure
activities of adults.
Joint frequency is the entries in the body of the two-way frequency table.
Joint relative frequency is the ratio of a frequency that is not in the total row or the total
column to the total number of values or observations.
Marginal frequency is the entry in the “total” for the column and the “total” for the row in
two-way frequency table.
Marginal relative frequency is the sum of the joint relative frequencies in a row or column.
Conditional frequency is when the body of two-way table contains relative frequencies.
1
Example 1: The table below shows the different activities that men and women can choose
to participate.
Dance
Men
2
Women 16
Total
18
Sport
10
6
16
TV
8
8
16
Total
20
30
50
Identify each of the following:
a) Joint frequencies are
b) Marginal frequencies are
Exercise 1 Answer the following questions for the given tables:
a) What are the marginal frequencies?
b) What are the joint frequencies?
2
Example 2. Find the joint relative frequency and marginal relative frequency for the
following table from Example 1.
Dance
Men
2
Women 16
Total
18
Sport
10
6
16
TV
8
8
16
Total
20
30
50
TV
Total
Relative and Marginal Frequency Table
Dance
Sport
Men
Women
Total
3
Exercise 2: Find the joint relative frequency and marginal relative frequency for the
following table from Exercise 1.
Relative and Marginal Frequency Table
Drinking and Gender of 212 Students
Gender
Female
None
Some
Lots
Totals
Male
Totals
4
EXIT
1. Copy the answer from the DO NOW and find the joint and marginal frequencies for
the data.
Freshmen
Sophomores
Total
Attending
25
80
Not Attending
Total
69
32
Joint and Marginal Frequency Table
Attending
Not Attending
Total
Freshmen
Sophomores
Total
2. Find the measure of the reference angle.
480°
5
Lesson 48
Mr. Jones
Trigonometry
Name:_______________________
Date:___________________
Homework
1. A public opinion survey explored the relationship between age and support for
increasing the minimum wage. The results are summarized in the two-way table to the
right. In the 21 to 40 age group, what percentage supports increasing the minimum
wage?
For
Against
No opinion
Total
21 - 40
25
20
5
50
41 - 60
20
35
20
75
Over 60
55
15
5
75
Total
100
70
30
200
a) What is the joint frequency for people in the age group 41-60 who are against
increasing the minimum wage?
b) What is the marginal frequency for persons with no opinion?
c) Find the joint relative and marginal relative frequencies for the minimum wage
data.
For
Against
No opinion
Total
21-40
41-60
Over 60
Total
6
2.
3.
7