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.

Section 1.2 Comparing Distributions

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.

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

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

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:

Fat Absorption

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.

Now let’s compare… Fat Absorption

Study habits and attitude test scores for freshmen men and women. 154 137 152 101 126 165 200 109 115 140 178 103 129 148 Men 108 114 180 126 169 109 75 113 70 187 140 91 115 92 146 132 88 151 104 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.

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