1. Two-Way Frequency Tables 8.SP.4 Essential Question? How can you construct and interpret two-way frequency tables?

2. Common Core Standard: 8.SP ─ Investigate patterns of association in bivariate data. 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two- way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

3. Objectives: To construct and interpret two-way frequency tables.

4. Curriculum Vocabulary Conditional Relative Frequency (frecuencia relativa condicional) : The ratio of a joint relative frequency to a related marginal relative frequency in a two-way table. Frequency (frecuencia): The number of times the value appears in the data set. Joint Relative Frequency (frecuencia relativa conjunta) : The ratio of the frequency in a particular category divided by the total number of data values. Marginal Relative Frequency (frecuencia relativa marginal) : The sum of the joint relative frequencies in a row or column of a two-way table.

5. Curriculum Vocabulary Relative Frequency (frecuencia relativa): The frequency of a specific data value divided by the total number of data values in the set. Two-way Table (de dos vías mesa): A table that displays two-variable data by organizing it into rows and columns. Two-way Relative Frequency Table ( dos vías tabla de frecuencias relativas) : A two-way table that displays relative frequencies.

6. Two-Way Frequency Tables The FREQUENCY of an event is the number of times the event occurs. A TWO-WAY TABLE shows the frequencies of data that is categorized two ways. The rows indicate one categorization and the columns indicate another.

7. Making a Two-Way Table A poll of 120 town residents found that 40% own a bike. Of those who own a bike, 75% shop at the farmer’s market. Of those who do not own a bike, 25% shop at the farmer’s market. STEP 1: Start in the bottom right cell of the table. Enter the total number of people polled. STEP 2: Fill in the right column. 40% of 120 people own a bike. STEP 3: Fill in the top row. 75% of those who own a bike also shop at the market. (the remaining bike owners do not shop at the market) Farmer’s Market No Farmer’s Market TOTAL Bike No Bike TOTAL 120 48 72 3612

8. Making a Two-Way Table A poll of 120 town residents found that 40% own a bike. Of those who own a bike, 75% shop at the farmer’s market. Of those who do not own a bike, 25% shop at the farmer’s market. STEP 4: Fill in the second row. 25% of those who do not own a bike shop at the market. (the remaining people without bikes do not shop at the market) STEP 5: Fill in the last row. In each column, add the numbers in the first two rows to find the total number of people in each category. Farmer’s Market No Farmer’s Market TOTAL Bike No Bike TOTAL 120 48 72 3612 1854 66 How can you check that your table is completed correctly?

9. Deciding Whether There is Association? RELATIVE FREQUENCY is the RATIO of the number of times an event occurs to the total number of events. Farmer’s Market No Farmer’s Market TOTAL Bike No Bike TOTAL 120 48 72 3612 1854 66 You can use RELATIVE FREQUENCIES to decide if there is an association between two variables or events.

10. Deciding Whether There is Association? Determine whether there is a association between the events. CurfewNo CurfewTOTAL Chores16420 No Chores166480 TOTAL3268100 One hundred teens were polled about whether they are required to do chores and whether they have a curfew. Is there an association between having a curfew and having to do chores?

11. Deciding Whether There is Association? Determine whether there is a association between the events. CurfewNo CurfewTOTAL Chores16420 No Chores166480 TOTAL3268100 One hundred teens were polled about whether they are required to do chores and whether they have a curfew. Is there an association between having a curfew and having to do chores?

12. Deciding Whether There is Association? Determine whether there is a association between the events. LateNot LateTOTAL Domestic30120150 International104050 TOTAL40160200 Data from 200 flights were collected. The flights were categorized as domestic or international and late or not late. Is there an association between international flights and a flight being late?

13. Deciding Whether There is Association? Determine whether there is a association between the events. LateNot LateTOTAL Domestic30120150 International104050 TOTAL40160200 Data from 200 flights were collected. The flights were categorized as domestic or international and late or not late. Is there an association between international flights and a flight being late?

14. Data from 200 middle school and high school students were collected. Students were asked whether or not they had visited at least one national park. Is there an association between being a high school student and visiting a national park? Explain. Have Visited a National Park Have NOT Visited a National Park TOTAL Middle School 255580 High School 8040120 TOTAL10595200

15. In a survey of 50 students, 60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. Complete the two-way table. DogNo DogTOTAL Cat No Cat TOTAL

16. The table gives partial information on the number of men and women who play in the four sections of the Metro Orchestra. StringsBrassWoodwindsPercussionTOTAL Men Women TOTAL 1.Complete the table. 2.Is there an association between being a woman and playing strings?