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. Using the above conditional distributions, is there is a relationship between gender and backpack use for the students in the sample?

a. YESb. NO

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 two __________; or one stacked bar graph.

25. Graph the conditional distributions of backpack use for 1) the males and 2) the females using two bar graphs.

Gender and # friends on Facebook

Everyone is studying how people are using the social media. Below are the results of one large study of Facebook users; they studied gender (male, female, and unspecified) and number of friends (1, 2-25, 25-60, …, 10,000+), for all those users who have at least one friend. Use this data to answer the questions below the data set. IMPORTANT NOTES:

Gender has 3 categories: 1) male; 2) female; and 3) unspecified. We assume all Facebook users in this study have at least one friend. At least one friend = Those with 1 friend + Those with more than 1 friend Grand totals for those with at least one friend are at the very bottom of the data table.

# Friends and Gender

# People

Women that have only 1 friend

2,958,499

Men that have only 1 friend

2,724,131

Unspecified gender that have only 1 friend

1,237,577

Total number that have only 1 friend

6,920,207

Women that have 2-25 friends

6,863,667

Men that have 2-25 friends

6,232,222

Unspecified gender that have 2-25 friends

1,612,446

Total number that have 2-25 friends

14,708,335

Women that have 26-50 friends

1,519,896

Men that have 26-50 friends

1,339,182

Unspecified gender that have 26-50 friends

164,784

Total number that have 26-50 friends

3,023,862

Women that have 51-100 friends

1,713,875

Men that have 51-100 friends

1,488,712

Unspecified gender that have 51-100 friends...

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