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Comparing Distributions: Jury Awards and Study Habits in Chicago

Explore the great difference between median and mean jury awards in civil cases in Chicago, and compare study habits between men and women using SSHA scores. Determine if the data supports women studying more than men and predict the placement of a new woman in the distribution.

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Comparing Distributions: Jury Awards and Study Habits in Chicago

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  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. Section 1.2 Comparing Distributions

  3. 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.

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

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

  6. 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:

  7. Fat Absorption

  8. 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.

  9. Now let’s compare… Fat Absorption

  10. Study habits and attitude test scores for freshmen men and women. Draw a graph of the distributions, then compare men and women’s SSHA scores. Does this data support the argument that women study more than men? If another woman was added to the appropriate data set with a SSHA score of 150, where would she fall in the distribution? Give a good justification of how she compares to the other women in the study.

  11. Homework Study for QUIZ Tomorrow!

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