AP Statistics—unit 2 Exploring data

1. AP Statistics—unit 2Exploring data Unit 1 was all about producing data—collecting numbers with context. Now we start learning what to do with it all… (Click for the next slide)

2. Exploring data starts with… …pictures, pictures, pictures! • Bar Graphs • Pie Charts • Two-way (Contingency) Tables • Histograms • Dot Plots • Stem (and Leaf) Plots • Cumulative Relative Frequency Graphs (Ogives) (Click for the next slide)

3. Exploring data starts with… …pictures, pictures, pictures! • Bar Graphs • Pie Charts • Two-way (Contingency) Tables • Histograms • Dot Plots • Stem (and Leaf) Plots • Cumulative Relative Frequency Graphs (Ogives) • All graphs display the distribution of a variable of interest. In other words, they show the values the variable can take, and how often the variable takes each value. • These three graphs display categorical (qualitative) data. Let’s take a closer look… (Click for the next slide)

4. Bar Graphs Frequency (how many people responded) • One axis of a bar graph lists each of the categories • The other axis lists either the frequency (count) in each category OR the proportion (fraction/percentage) of observations in each category • The columns in a bar graph are separated by a little bit of space. They should not be right next to each other (unless the bar graph is comparing two categories) Categories (Click for the next slide)

5. Example 1 In 1997, there were 92,353 deaths from accidents in the United States. Among those were 42,340 deaths from motor vehicle accidents; 11,858 from falls; 10,163 from poisoning; 4,051 from drowning; and 3,601 from fires. *With such large numbers, it seems like a bar graph of the counts of deaths in each category would be hard to make—or at least rather cumbersome. So let’s graph the proportion of deaths in each category. 1) Determine what percent of deaths is accounted for in each category. (click for answer) Notice that the sum of the causes listed is not 92,353. You need to include an “Other” category to account for the “unused” data. (Click for the next slide)

6. Example 1 Continued Start by labeling your graph with categories and intervals for the proportions Then draw in boxes at the appropriate height for each category. Remember: make them the same width so you don’t violate the area principle! Your bar graph is done! We don’t use SOCS on bar graphs--it just doesn’t make sense! (Click for the next slide)

7. Pie charts A good pie chart for the accidental deaths. • Each piece of the pie represents the proportion of responses that fall in a category • The total percentage (proportion) of data used to create the pie chart must be 100%! • Don’t violate the area principle! It’s easy to do for “artistic” reasons. A bad pie chart for the accidental deaths. (Click for the next slide)

8. Pie charts • You will never need to create a pie chart by hand • Excel created the two on the previous slide, and other programs do a great job as well • You should be able to read, interpret, and identify which pieces of the pie represent which categories. (Click for the next slide)

9. Two-way (contingency) Tables 50 students were asked whether or not they were taking a foreign language and whether or not they played a sport. The results of the survey are summarized in the two-way table below: (Click for the next slide)

10. Two-way (contingency) Tables Two-way tables are called such because they contain a “row” variable and a “column” variable. ColumnVariable RowVariable • The distributions on the edges (margins) are called “marginal distributions” and summarize the distribution of only one variable. Marginal distributions are often summarized as proportions instead of counts. • For instance, the marginal distribution at the bottom summarizes the column variable. That is, 24/50 (0.48) students play a sport and 26/50 (.52) do not, but it tells us nothing about if they take a foreign language. (Click for the next slide)

11. Two-way (contingency) Tables It’s the conditional distributions that are interesting. Conditional distributions exam single rows or single columns at a time. If we examine only the top row, we can see that, if students take a foreign language, they are more likely to not play a sport (23/37 vs. 14/37). This is called a conditional distribution because we are examining the distribution of values under the condition that the respondents took a foreign language. (Click for the next slide)

12. Example ii Hannah surveyed students in the cafeteria about the number of times they bring their lunch to school per month. She used the two-way table below to summarize her findings: Find the marginal distribution of how often students bring their lunch in proportions. Determine the conditional distribution for males and the conditional distribution for females. What (if any) conclusions can you draw? (Click for the next slide)

13. Example ii Hannah surveyed students in the cafeteria about the number of times they bring their lunch to school per month. She used the two-way table below to summarize her findings: a) (Click for the next slide)

14. Example ii b) • If you are male, you are more likely to bring your lunch to school 16-20 times a month, while females are more likely to bring their lunch only 0-5 times per month (Click for the next slide)

15. Tomorrow You’ll Learn more about quantitative displays and analysis. There will also be an assignment on mymathlab. I’ll send a reminder when they are posted!Holla at me with ways to make these betterpeace That’s all Folks!