Two-way tables can be used to examine relationships between two variables. Suppose we have data on 200 students regarding their gender and whether or not they wear backpacks to school. The data is summarized in the two-way table below. 2. Fill in the remaining numbers in the table. Backpack: Yes Backpack: No Male Female Different ways to summarize the data from a two way table distribution summarizes the data from one variable only. 4. Find the marginal distribution of gender: 5. Interpretation: 6. Find the marginal distribution of backpack use: .

Interpretation: 8. Note: the sum of all the percentages in a marginal distribution equals Graphing a marginal distribution: 9. Graphical versions of a marginal distribution can be done using a showing the percentage in each group. 10. Graph the marginal distribution of gender using a pie chart: or a 1 1 . Graph the marginal distribution of backpack use using a bar graph: How do we look for relationships between two categorical variables? 12. Big Idea: Break down the data into groups and compare the results of each group. This involves finding a distribution. 3.

To look for relationships between two variables you can find the two distributions and them to each other. 14. If the results of each group are the same, then the two variables are / are not related. (pick one). 15. Find the conditional distribution of backpack use for the males: 16. **Another way of describing the above distribution is to say this is the conditional distribution of given 17. Interpretation of the previous graph: 18. Find the conditional distribution of backpack use given female: 19. Interpretation: Making the comparisons: 20. You can look for relationships between two variables by comparing their distributions. 1 . Using the above conditional distributions, is there is a relationship between gender and backpack use for the students in the sample? B. NO a. YES 22. Justify your YES or NO answer: 23. If there IS a relationship, describe the relationship using percentages in a sentence or two. Comparing Conditional Distributions using Graphs 24. Graphing 2 conditional distributions can be done using two or one stacked bar graph. Or two 25. Graph the conditional distributions of backpack use for 1) the males and 2) the males using two bar graphs. Gender and # friends on Faceable Everyone is studying how people are using the social media.