2. Unit 4 Lesson 8 Demonstrating Mastery

3. M.8.SP.4 To demonstrate mastery of the objectives in this lesson you must be able to: 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.

4. Performance Task for Demonstration of Mastery Task Members of the student council, Emma and Isaiah, were concerned about a new dress code at school. They decided to conduct a survey and collect some data. They recorded two pieces of data from 317 students: gender and whether or not they agreed with the school’s new dress code. They found 82 boys who agreed, 73 boys who disagreed, 59 girls who agreed, and 103 girls who disagreed.  Construct and interpret a two-way table for the categorical data  Calculate the relative frequencies for the data set  Use the relative frequencies to describe possible association between the two variables

5. Two-Way Frequency Table Student Council Dress Code Survey Agree with Dress Code Disagree with Dress Code Totals Boys 82 73 155 Girls 59 103 162 Total 141 176 317

6. Two-Way Relative Frequency Table Student Council Dress Code Survey (column) Agree with Dress Code Disagree with Dress Code Totals Boys 82 ≈ 0.58 58% 73 ≈0.41 41% 155 ≈0.49 49% Girls 59 ≈0.42 42% 103 ≈0.59 59% 162 ≈0.51 51% Total 141 100% 176 100% 317 100%

7. Two-Way Relative Frequency Table Student Council Dress Code Survey (row) Agree with Dress Code Disagree with Dress Code Totals Boys 82 ≈ 0.53 53% 73 ≈0.47 47% 155 100% Girls 59 ≈0.36 36% 103 ≈0.64 64% 162 100% Total 141 ≈0.44 44% 176 ≈0.56 56% 317 100%

8. Two-Way Frequency Table Student Council Dress Code Survey Agree with Dress Code Disagree with Dress Code Totals Boys 82 73 155 Girls 59 103 162 Total 141 176 317

9. Two-Way Relative Frequency Table Student Council Dress Code Survey (column) Agree with Dress Code Disagree with Dress Code Totals Boys 0.58 0.410.49 Girls 0.42 0.59 0.51 Total 1.00

10. Two-Way Relative Frequency Table Student Council Dress Code Survey (row) Agree with Dress Code Disagree with Dress Code Totals Boys 0.530.471.00 Girls 0.360.64 1.00 Total 0.440.561.00

11. Summary of Findings  More girls disagree with the dress code than boys.  Almost twice as many girls disagree than agree.  The boys are closely divided concerning the dress code.  Overall more students disagree with the dress code.  The column relative frequency indicates that there is no association between the variables.  If the surveyed person is a girl, there is a 64% chance that she will disagree with the dress code.