1. Two-Way Tables
Skill 18

2. Objectives Understand what is a two-way frequency table.
Properly use a two-way frequency table.
Properly construct a two-way frequency table.

3. Example- Two-Way Table
An insurance company selected drivers in a particular city to find a relationship between the age of the driver and the number of car accidents. Complete the following table.
Age of Driver
Accidents in Year
(in years) 1 2 3
Total
17 – 25 15 23 40
26 – 40 50 44 56
Above 40 62 22 11 78
150 95
127 89
107
323

4. Example-Complete the questions
A) Find the probability of total accidents attributed to the 17 to 25 year old age group of drivers.
Solution:
P(17 to 25 yr. old)
= (17 to 25 yr. old)
Total
= 78
323
= .24 = 24%
B) Find the probability of an accident in year 2 was attributed to the 26 to 40 year old age group of drivers.
Solution:
P(26 to 40 yr. old | yr. 2)
= (26 to 40 yr. old)
Year 2
= 44 89
= .494 = 49.4%

5. Example- Two-Way Table
An insurance company selected drivers in a particular city to find a relationship between the age of the driver and the number of car accidents. Complete the following table.
Boys
Girls
Total
Cooking 15 30
Dancing 40 35
Painting 33 38
Other 42 39 45 75 71 81
130
142
272

6. Example-Complete the questions
A) What is the probability of all the students that joined the dance class?
Solution:
P(Dance)
= All Dance
Total
= 75
272
= = 27.57%
B) What is the probability that the person picked is girl that joined the painting class?
Solution:
P(Girl and Painting)
= Girl Painting
Total
= 38
272
= = 13.97%

7. Example-Complete the questions
A) What is the probability that given we know the person is a boy, he joined the painting class?
Solution:
P(Painting | Boy)
= Boy Painting
Total Boy
= 33
130
= = 25.38%

8. 20 52 72 25 15 40 77 35 112 Example- Two-Way Table Students Full-Time
A survey was conducted for part-time and full-time boys and girls enrolled at Henkey College. It was found that the total number of boys enrolled was 72. From these 52 boys were full-time. There were 25 full-time girls and 15 part-time girls.
Create a two-way table using the information above.
Students
Full-Time
Part-Time
Total
Boys
Girls 20 52 72 25 15 40 77 35
112

9. 25 14 39 16 5 21 30 30 60 Example- Two-Way Table Students
Students were planning on going on a school picnic. The teacher was taking a survey of who was going and who was not. She found that of the 39 boys in the class, 14 were planning on attending the picnic. Also, of the 21 girls in the class, 5 were not going to the picnic.
Create a two-way table using the information above.
Students
Going to Picnic
Not Going to Picnic
Total
Boys
Girls 25 14 39 16 5 21 30 30 60

10. 20 18 33 35 32 67 50 50 100 Example- Two-Way Table Students
It was found that 33 students are taking math, and 18 of those students are not taking physics. Sixty-seven students are not taking math, but 35 of those students are taking physics.
Create a two-way table using the information above.
Students
Physics Class
Not in Physics
Total
Math Class
Not in Math 20 18 33 35 32 67 50 50
100

11. 18: Two-Way Tables
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Homework
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