1. Warm-up A study of the size of jury awards in civil cases (such as injury, product liability, and medical malpractice) in Chicago showed that the median award was about $8,000. But the mean award was about $69,000. Explain how this great difference between the two measures of center can occur.

2. Warm up Pg. 77 #R1.9

3. Ogives and Timeplots O-What???

4. Ogives Pronouced Oh-Jives An ogive is a relative cumulative frequency graph. Oh, that’s crystal clear! Oh, that’s crystal clear!

5. Frequency Tables This data set lists the number of books that are on the desks of 50 college students at 8:00 a.m. on Monday morning. Using this data, count how many times each value occurs. Make a tally chart. 351046 7212119 75348 5109147 21057 89141810 16785 3101234 22643 510996

6. Frequency and Relative Frequency Frequency simply means how many times a certain value occurs. Your tally marks represent the frequency. Relative frequency means you convert the number of tally marks to a percent of the total. i.e. divide by 50

7. Relative Frequency ValueFrequency 01 1/50 =.02 = 2% 12 2/50 =.04 = 4% 24 4/50 =.08 = 8% 35 5/50 =.10 = 10% 44 4/50 =.08 = 8%

8. Cumulative Frequency Cumulative frequency tells us how many values fall at or below a certain number! Simply add your tally marks from the lowest value up to calculate cumulative frequency. ValueFrequency Relative Frequency Cumulative Frequency 01 1/50 =.02 = 2% 1 12 2/50 =.04 = 4% 3 24 4/50 =.08 = 8% 7 35 5/50 =.10 = 10% 12 44 4/50 =.08 = 8% 16

9. Cumulative Frequency vs. Relative Frequency Cumulative frequency – quantity. Relative cumulative frequency is the percent of data that fall at or below a given value. This is also called a PERCENTILE, which is a word you will hear frequently.

10. Relative Frequency ValueFrequency Cumulative Frequency Relative Cumulative Frequency 01 1/50 =.02 = 2% 1 12 2/50 =.04 = 4% 3 3/50 =.06 = 6% 24 4/50 =.08 = 8% 7 7/50 =.14 = 14% 35 5/50 =.10 = 10% 12 12/50 =.24 = 24% 44 4/50 =.08 = 8% 16 16/50 =.32 = 32%

12. THIS is an ojive!

13. So what’s the point? We are able to tell where an individual in a population stands relative to others. Example… Look at your graph. What percent of students have no more than 10 books on their desk Monday morning?

14. About 88%.

15. How many books do 40% of the students have on their desks Monday morning?

16. Time Plots Shows each observation at the time it was measured. The time scale is on the horizontal axis. The variable of interest (temperature, stock prices, gasoline prices) is on the vertical axis. Look for a trend, or an overall pattern.

17. Section 1.2 Comparing Distributions

18. Comparing Distributions Often, the question of interest is which car/drug/fuel additive etc. is preferable. In this case, we need to be able to compare distributions.

19. Graph Choices for Comparing Distributions For categorical variables, a side- by-side bar graph works well.

20. Graph Choices for Comparing Distributions For two small quantitative data sets, a back-to- back stem and leaf plot is effective.

21. Graph Choices for Comparing Distributions Boxplots alone contain little detail, but side-by-side boxplots effectively compare large sets of quantitative data. The plot is useful for showing the comparison of several groups. This example shows a fat absorption test in patients who have AIDS, AIDS Related complex, are HIV positive but asymptomatic, and normal controls:

22. Fat Absorption

23. Keys to Remember Plot both distributions using the same scale. Always compare apples to apples. By that, I mean compare mean to mean, median to median, Q1 to Q1, etc. Students lose points on the AP exam when they make comparisons between two different measures.

24. Now let’s compare… Fat Absorption

25. Homework Chapter 2 #2, 5, 7, 9, 10