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

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.

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.

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.

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?

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.

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

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.

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.

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.

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 2 + 38 + 7 + 3 = 50 people in the survey. Find the ratio of each frequency to the total number surveyed. Sick with Flu YES NO Flu Shot

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

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

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

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?