1. Core Focus on Linear Equations
Lesson 5.7
Core Focus on Linear Equations
Bivariate Data and Frequency Tables

2. Warm-Up Write each ratio as a fraction, decimal and percent.
1. Four out of five dentists recommend a particular type of chewing gum.
2. Thirteen out of every sixteen students have a cell phone.
3. Fourteen fish in an aquarium have stripes and six do not.
a) Write the ratio of striped fish to non-striped fish.
b) Write the ratio of striped fish to all fish in the aquarium.

3. Bivariate Data and Frequency Tables
Lesson 5.7
Bivariate Data and Frequency Tables
Describe associations between two sets of data using relative and conditional frequencies.

4. Vocabulary
Univariate Data Single-variable data, which describes one set of data. Bivariate Data Two-variable data, which looks at the relationship between two different sets of data. Categorical Data Data collected in the form of words or frequencies. Two-Way Frequency Table A table that shows how many times a value occurs for a pair of categorical data.

5. Good to Know!
 Bivariate data looks at the relationship between two different sets of data.
 The purpose of bivariate data is to explain relationships or causes.
For example, is there a relationship between the amount of absences a student has and the grade a student earns in class?

6. Good to Know!
Absences, x
Grade, y 95 86 91 1 85 90
100 88 2 87 3 70 7 75 9 72 10 65 20 50
What does the scatter plot below suggest about the relationship between a student’s absences and their grade in a class?
There is a negative correlation which suggests there is a relationship between the number of times a student is absent and the student’s grade.
The line of best fit is
y = –2x + 91.

7. Important Information:
Example 1
Marsha wanted to investigate a relationship between getting a flu shot and getting the flu. She asked fifty people if they had gotten a flu shot and whether or not they had been sick with the flu. Her data showed that 40 people had gotten a flu shot and 10 had not. Of the 40 with a flu shot, 2 had been sick with the flu. Of the 10 without a flu shot, 7 had been sick with the flu. Construct a two-way frequency table showing this information.
Important Information:
40 people had gotten the flu shot
Of the 40, 2 people had been sick
10 people had not gotten the flu shot
Of the 10, 7 people had been sick

8. Important Information:
Example 1 Continued…
Sick with Flu
YES NO
40 – 2 = 38
Flu Shot
10 – 7 = 3
Important Information:
40 people had gotten the flu shot
Of the 40, 2 people had been sick
10 people had not gotten the flu shot
Of the 10, 7 people had been sick
Determine the categories:
Construct a two-way frequency table.
Determine the frequencies in each pair of categories.

9. Vocabulary
Relative Frequency The ratio of the observed frequency to the total number of frequencies in an experiment or survey. Conditional Frequency The ratio of the observed frequency to the total number of frequencies within one category in an experiment or survey.

10. Examining Relationships Between Sets of Data
Relative Frequencies
Find the total number in the sample.
Calculate the ratio of each frequency to the total number sampled.
Conditional Frequencies
Find the total number sampled in one category.
Calculate the ratio of each frequency in that category to the total sampled in that category.

11. Example 2 Sick with Flu YES NO Flu Shot
a. Find the relative frequencies for the two-way table in Example 1. Determine the number of people = 50 people in the survey. Find the ratio of each frequency to the total number surveyed.
Sick with Flu
YES NO
Flu Shot

12. Example 2 Continued… YES NO 4% 76% 14% 6%
b. Explain one observation from the relative frequencies. One relative frequency shows 76% of those surveyed had a flu shot and did not get sick. It is likely a person asked will have had a flu shot and not gotten sick.
Sick with Flu
YES NO 4%
76%
14% 6%
Flu Shot

13. Example 2 Continued… YES NO 2 38 7 3
c. What is the conditional frequency that someone with a flu shot will not get sick? Find the number of people who had a flu shot. Find the ratio of the frequency to 40. According to this data, there is a 95% chance you will not get the flu if you have a flu shot.
Sick with Flu
YES NO 2 38 7 3
Flu Shot

14. Communication Prompt
Explain the difference between categorical data and numerical data.

15. Exit Problems
Twenty students were randomly selected to answer if they rode the bus to school and if they arrived to their first class on time.
 Of the 15 who rode the bus, 12 arrived on time.
 Two of those who did not ride the bus arrived on time.
1. Make a two-way frequency table to show the information.
2. What is the conditional frequency of a student who rides the
bus being late to class first period?