1. Two-Way Tables

2. Main Idea and New Vocabulary Example 1: Construct a Two-Way Table
Example 2: Relative Frequencies in a Two-Way Table
Example 3: Relative Frequencies in a Two-Way Table
Lesson Menu

3. Construct and interpret two-way tables.
relative frequency
Main Idea/Vocabulary

4. Construct a Two-Way Table
WATER PARK The eighth grade class went to a water park at the end of the year. Out of the 65 students who went to the park, 17 swam only in the wave pool. There were a total of 46 students who rode down the water slide and 16 of those also swam in the wave pool. Construct a two-way table summarizing the data.
Step 1 Create a table using the two categories: wave pool and water slide.
Wave Pool
No Wave Pool
Total
Water Slide
No Water Slide
Example 1

5. Construct a Two-Way Table
Step 2 Use the values given to fill in the table.
Wave Pool
No Wave Pool
Total
Water Slide
No Water Slide 16 46 17 65
Step 3 Use reasoning to complete the table. The totals are for each row and column.
Wave Pool
No Wave Pool
Total
Water Slide 16 46
No Water Slide 17 65 30 2 19 33 32
Example 1

6. A. Sixty-three students did not attend either activity.
Attended Play
Did Not Attend Play
Attended Basketball Game 55 63
Did Not Attend Basketball Game 88 15
ACTIVITIES Megan surveyed students to find which school activities they attended. The results are shown. Which statement is true?
A. Sixty-three students did not attend either activity.
B. Of the students that attended the basketball game, more than half of them did not attend the play.
C. Megan surveyed 200 students.
D. A total of 118 students attended the play.
Example 1 CYP

7. Relative Frequencies in a Two-Way Table
ENTERTAINMENT People at a movie theater were surveyed about whether they bought popcorn or soda. What is the relative frequency of people that bought both to all people that bought soda? Round to the nearest hundredth if necessary.
To find the relative frequencies by row, write the ratios of each value to the total in that row. Round to the nearest hundredth if necessary.
Example 2

8. Relative Frequencies in a Two-Way Table
Frequency by Row
Popcorn
No Popcorn
Total
Soda
No Soda
Answer: The relative frequency of people that bought both popcorn and soda to all people that bought soda is 0.6.
Example 2

9. PETS A pet store conducted a survey on the types of pets owned by the store’s customers. The results are shown in the two-way table.
Cat
No Cat
Total
Dog 45
125
170
No Dog 78 52
130
123
177
300
What is the relative frequency of customers that own both a cat and a dog to the total number of customers that own a dog?
A. about 0.26 C. about 0.63
B. about 0.37 D. about 0.74
Example 2 CYP

10. Relative Frequencies in a Two-Way Table
ENTERTAINMENT People at a movie theater were surveyed about whether they bought popcorn or soda. What is the relative frequency of people that did not buy either item to all people that did not buy popcorn? Round to the nearest hundredth if necessary.
When creating a two-way table with relative frequencies by column, use the total of the columns when writing the ratios.
Example 3

11. Relative Frequencies in a Two-Way Table
Frequency by Column
Popcorn
No Popcorn
Total
Soda
No Soda
Answer: The relative frequency of people that did not buy either item to all people that did not buy popcorn is 0.41.
Example 3

12. PETS A pet store conducted a survey on the types of pets owned by the store’s customers. The results are shown in the two-way table.
Cat
No Cat
Total
Dog 45
125
170
No Dog 78 52
130
123
177
300
What is the relative frequency of customers that neither own a cat nor a dog to the total number of customers that do not own a cat?
A. about 0.71 C. about 0.37
B. about 0.63 D. about 0.29
Example 3 CYP

13. Two-Way Tables