ADAPTED FROM WALCH EDUCATION Using Two-Way Frequency
Tables
Slide 3
Previously, you learned that there are two equivalent
expressions for the conditional probability of B given A:
Conditional probability can be used to test for independence.
Events A and B are independent events if or if Key Concepts 7.2.2:
Using Two-Way Frequency Tables2
Slide 4
For real-world data, modified tests for independence are
sometimes used: Events A and B are independent if the occurrence of
A has no significant effect on the probability of B; that is,
Events A and B are independent if the occurrence of B has no
significant effect on the probability of A; that is, Continued
7.2.2: Using Two-Way Frequency Tables3
Slide 5
If A and B are two events from a sample space with P(A) 0, then
the conditional probability of B given A in set notation is The
conditional probability formula can be solved to obtain this
formula for P(A and B): Concepts, continued 7.2.2: Using Two-Way
Frequency Tables4
Slide 6
A two-way frequency table is a frequency table that shows two
categories of characteristics, one in rows and the other in
columns. Each cell value is a frequency that shows how many times
two different characteristics appear together. Two-Way Frequency
Table 7.2.2: Using Two-Way Frequency Tables5
Slide 7
Typical Setup of a Two-Way Frequency Table 7.2.2: Using Two-Way
Frequency Tables6 Category 1 of characteristics Category 2 of
characteristics Characteristic 1Characteristic 2 Characteristic 1ab
Characteristic 2cd
Slide 8
When probabilities and conditional probabilities are
calculated, then totals of characteristics are needed. Note: 7.2.2:
Using Two-Way Frequency Tables7 Category 1 of characteristics
Category 2 of characteristicsTotal Characteristic 1Characteristic 2
Characteristic 1ab Characteristic 2cd Total
Slide 9
The Student Council wants to host a school-wide activity.
Council members survey 40 students, asking them to choose either a
field trip, a dance, or a talent show. The table on the following
slides shows the survey results, with the surveyed students
numbered 140. Construct a two-way frequency table to summarize the
data. Practice: 7.2.2: Using Two-Way Frequency Tables8
Slide 10
Table of Survey Results 7.2.2: Using Two-Way Frequency Tables9
(continued) StudentGradeActivityStudentGradeActivity 110FT1112D 2 D
10TS 310TS1311TS 410FT1410FT 511D1511D 612D1610FT 710TS1712D
810FT1810FT 910FT1912D 1011TS2011TS Key: TS = Talent show, FT =
Field trip, D = Dance
Slide 11
Table of Survey Results, continued 7.2.2: Using Two-Way
Frequency Tables10 StudentGradeActivityStudentGradeActivity
2110D3112FT 2210FT3210TS 2312D3312D 2411D3411D 2511TS3511FT
2612D3611FT 2712D3711TS 2810D3812TS 2911D3911FT 3011D4012TS Key: TS
= Talent show, FT = Field trip, D = Dance
Slide 12
Set up a table that shows Grade and Activity choice as
categories, and all the different characteristics in each category.
Step 1 7.2.2: Using Two-Way Frequency Tables11 Grade Activity
choice Talent showField tripDance 10 11 12
Slide 13
For each student, draw a tally mark that corresponds to that
students grade and choice of activity in the appropriate cell of
the data table. The complete tally table below shows the tally
marks for all the students. Step 2 7.2.2: Using Two-Way Frequency
Tables12 Grade Activity choice Talent showField tripDance 10 11
12
Slide 14
Create a two-way frequency table to show your count results
(These results are frequencies). Step 3 7.2.2: Using Two-Way
Frequency Tables13 Grade Activity choice Talent showField tripDance
10482 11536 12219