1. NC Common Core Standards
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.
Objectives
Create: relative frequency, two-way frequency, and two-way relative frequency tables, in addition to recognizing associations and trends

2. Glossary Terms:
Two-way Frequency table: a table listing two categorical variables who values have been paired.

3. Creating a Relative Frequency Table:
Jenna asked 40 randomly selected students whether they preferred dogs, cats or other pets.
Complete the table for both decimals and percents
Preferred Pet
Dog
Cat
Other
Total
Frequency 18 12 10 40
Relative Frequency Decimals
Relative Frequency Percents
= .45
= .30
= .25
= 1.00
45%
30%
25%
100%

4. Creating a Two-Way Frequency Table:
Jenna also recorded the gender of each student.
The results are shown in the two-way frequency table. Find the totals and answer the questions.
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 12 10 40
1) How many total students took the survey? 40
2) How many total boys took the survey? 24
3) How many students said they like dogs as pets? 18
4) How many boys said they like dogs as pets? 10

5. Creating a Two-Way Relative Frequency Table:
Jenna also recorded the gender of each student surveyed, complete the two-way frequency table below.
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 12 10 40
Preferred Pet
Dog
Cat
Other
Total
Boys
Girls
Totals
= .25
= .125
= .225
= .60
= .20
= .175
= .025
= .40
= .45
= .30
= .25
= 1.00

6. Creating a Two-Way Relative Frequency Table:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Relative Frequency Table:
Preferred Pet
Dog
Cat
Other
Total
Boys
Girls
Totals
= .25
= .125
= .225
= .60
= .20
= .175
= .025
= .40
= .45
= .30
= .25
= 1.00
State the percents for the table above.
Preferred Pet
Dog
Cat
Other
Total
Boys
Girls
Totals
25%
12.5%
22.5%
60%
20%
17.5%
2.5%
40%
45%
30%
25%
100%

7. Creating a Two-Way Relative Frequency Table:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Creating a Two-Way Relative Frequency Table:
Preferred Pet
Dog
Cat
Other
Total
Boys
25%
12.5%
22.5%
60%
Girls
20%
17.5%
2.5%
40%
Totals
45%
30%
100%
1) Find the joint relative frequency of students surveyed who are girls and prefer dogs as pets.
20%
2) Find the joint relative frequency of students surveyed who are boys and prefer cats as pets.
12.5%
3) Find the marginal RF of students surveyed who prefer dogs as pets and then prefer cats as pets.
dogs - 45%
cats - 30%

8. Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 12 10 40
Find the conditional relative frequency that a student surveyed prefers cats as pets, given the student is a girl.
Number of girls who prefer cats: 7
= .4375
= 43.75%
Number of girls: 16

9. Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 10 40 12
Find the conditional relative frequency that a student surveyed is a girl, given that the student prefers cats as pets.
Number of girls who prefer cats: 7
= .583
= 58.3%
Number of students who prefer cats: 12

10. Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 12 10 40
Find the conditional relative frequency that a student surveyed prefers cats as pets, given the student is a boy.
Number of boys who prefer cats: 5
= .208
= 20.8%
Number of boys: 24

11. Calculating a Conditional Relative Frequency:
Old Holt 4-5/4-6; New Holt 10-1/10-2/ On-Core: 9-5 Two Way Frequency Tables
Calculating a Conditional Relative Frequency:
Preferred Pet
Dog
Cat
Other
Total
Boys 10 5 9 24
Girls 8 7 1 16
Totals 18 10 40 12
Find the conditional relative frequency that a student surveyed is a boy, given that the student prefers dogs as pets.
Number of boys who prefer dogs: 10
= .556
= 55.6%
Number of students who prefer dogs: 18