# Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.5

Twenty adult males between the ages of 30 and 40 were involved in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control group and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The following data show the reduction in cholesterol experienced for the time period for the 20 subjects:

 Control Group 7 3 -4 14 2 5 22 -7 9 5 Treatment Group -6 5 9 4 4 12 37 5 3 3

(a) Do a dot plot of the data for both groups on the same graph.

(b) Compute the mean, median, and 10% trimmed means for both groups.

(c) Explain why the difference in the mean suggests one conclusion about the effect of the regimen, while the difference in medians or trimmed means suggests a different conclusion.

## Solution:

Part (a)

A dot plot is shown below

Part (b)

The mean, median, and 10% trimmed mean of the control group are

$\displaystyle \overline{x}_{control}=5.60$

$\displaystyle \widetilde{x}_{control}=5.00\:$

$\displaystyle \overline{x}_{tr\left(10\right);control}=5.13$

The mean, median, and 10% trimmed mean of the treatment group are

$\displaystyle \overline{x}_{treatment}=7.60$

$\displaystyle \widetilde{x}_{treatment}=4.50\:$

$\displaystyle \overline{x}_{tr\left(10\right);treatment}=5.63$

Part (c)

The diﬀerence of the means is 2.0 and the diﬀerences of the medians and the trimmed means are 0.5, which are much smaller. The possible cause of this might be due to the extreme values (outliers) in the samples, especially the value of 37.