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1. 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
30
60

Female
30
80

Different ways to summarize the data from a two way table
3. A _______ 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:

7. 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 _________ or a __________ showing the percentage in each group.

10. Graph the marginal distribution of gender using a pie chart:

11. 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.

13. 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.

21.

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