1. CrimiNole Gatorbait OR ? Are you a Two rivalries in one table! Two rivalries in one table! !

2. Garnet and Gold or Orange and Blue? You decide! Garnet and Gold Orange and Blue Total Males6410 Females10313 Total16723 How many males like orange and blue? What does the number 16 represent? How many people were surveyed? How would you determine if there was a possible association between favorite team colors and gender? A survey was conducted and the results are shown in the table below. Try to answer the following questions.

3. Two-Way Frequency Tables

4. Florida Standard MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in data.

5. Objectives Create and interpret a two-way frequency table from two categorical variables. Read and interpret data displayed in a two-way table and calculate the relative frequencies. Describe patterns and trends observed in the data.

6. What is a two-way frequency table? TOTAL 81321 112132 193453 LOOKS LIKE CATEGORY B CATEGORY A Two-Way Table A table used to study the relationship between two categorical variables.

7. Joint and Marginal Frequency TOTAL CATEGORY A CATEGORY B 813 112132 5334 19 21 Joint Frequency The values that make up the BODY of the table. Marginal Frequency The ROW and COLUMN totals for each category.

8. 25 seniors were surveyed and asked which college football team they liked best. Out of the 17 that liked Florida State, 6 were females. There was a total of 13 females surveyed. Summarize the data in a two-way table. Florida State Florida Total Males Females Total Ex. 1 Construct a Two-Way Table Fill in the values you already know. Determine if each value represents a JOINT or MARGINAL frequency. Recall that JOINT frequency goes in the body (yellow area) of the table, and MARGINAL frequency goes in the row and column total (green area) of the table. Use reasoning to find the remaining values. TIPS FOR COMPLETING THE TABLE

9. Guided Practice Construct a Two-Way Table There were 45 students in gym class that were asked if they like football or basketball and if they liked Nike or Adidas. Out of the 19 students that liked basketball, 7 liked Adidas. There were 23 students that liked Adidas. Use reasoning to find the missing values. NikeAdidasTotal Football Basketball Total

10. Calculate Row Relative Frequencies Relative frequency is the ratio of the subtotal to the total Florida State Florida Total Males 11112 Females 6713 Total 17825 For each row, find the ratio of each joint frequency to the marginal frequency for that row. Florida State Florida Total Males Females Total The relative frequencies in the body of the table are called conditional relative frequencies.

11. Calculate Column Relative Frequencies Relative frequency is the ratio of the subtotal to the total Florida State Florida Total Males 11112 Females 6713 Total 17825 For each column, find the ratio of each joint frequency to the marginal frequency for that column. Florida State Florida Total Males Females Total

12. Guided Practice Calculate Relative Frequencies Calculate the missing row relative frequencies for the table. Round to the nearest hundredth. Show all work. Calculate the missing column relative frequencies for the table. NikeAdidasTotal Football Basketball Total NikeAdidasTotal Football Basketball Total

13. Association between two categorical variables occur when the conditional relative frequencies for the rows or columns differ significantly. There is little to no association between two categorical variables when the conditional relative frequencies for the rows or columns are equal or evenly distributed.

14. Read, Interpret, and Draw Conclusions Two-Way Frequency Florida State Florida Total Males 11112 Females 6713 Total 17825 Which table can we use to determine the percentage of males that like Florida? What is the percentage? Which table can we use to determine the percentage of females that took the survey? What is the percentage? [ROW] Relative Frequencies Florida State Florida Total Males 0.920.081.00 Females 0.460.541.00 Total 0.680.321.00 [COLUMN] Relative Frequencies Florida State Florida Total Males 0.650.130.48 Females 0.350.880.52 Total 1.00 Use the tables to answer the following questions. Based on the row conditional frequencies, is there evidence of an association between gender and favorite college football team? What do the numbers 7, 11, and 12 represent? Are they JOINT or MARGINAL frequencies?

15. Guided Practice Read, Interpret, and Draw Conclusions Refer back to the tables in problem 1 & 2 to answer the following questions. 1. What is the joint frequency of students who like Nike? 2. What is the marginal frequency of students who like basketball? 3. Of the students who like Nike, what percentage like football as well? 4. What percentage of the students like basketball and Adidas? 5. Is there evidence of an association between the sport a student likes and the brand of sneakers they like? Explain.

16. What have you learned? Refer back to the opening problem. Answer the questions again. How do your “post lesson” answers compare to your “pre-lesson” answers? Are they the same or different? How many males like orange and blue? What does the number 16 represent? How many people were surveyed? How would you determine if there was a possible association between favorite team colors and gender? A survey was conducted and the results are shown in the table below. Answer the following questions. Garnet and Gold Orange and Blue Total Males 6410 Females 10313 Total 16723