Question

For each of the following data sets, construct a graphical display of the data distribution and then indicate what summary measures you would use to describe center and spread. a. The following are data on weekend exercise time for 20 females consistent with summary quantities given in the paper "An Ecological Momentary Assessment of the Physical Activity and Sedentary Behaviour Patterns of University Students" (Health Education Journal [2010]: \(116-125)\) Female-Weekend \(\begin{array}{lrrrrrr}84.0 & 27.0 & 82.5 & 0.0 & 5.0 & 13.0 & 44.5 \\ 3.0 & 0.0 & 14.5 & 45.5 & 39.5 & 6.5 & 34.5 \\ 0.0 & 14.5 & 40.5 & 44.5 & 54.0 & 0.0 & \end{array}\) b. The accompanying data are consistent with summary statistics that appeared in the paper "Shape of Glass and Amount of Alcohol Poured: Comparative Study of Effect of Practice and Concentration" (British Medical Journal [2005]: 1512-1514). Data represent the actual amount (in \(\mathrm{ml}\) ) poured into a tall, slender glass for individuals asked to pour a "shot" of alcohol \((44.3 \mathrm{ml}\) or 1.5 ounces). \(\begin{array}{lllllll}44.0 & 49.6 & 62.3 & 28.4 & 39.1 & 39.8 & 60.5 \\ 73.0 & 57.5 & 56.5 & 65.0 & 56.2 & 57.7 & 73.5 \\ 66.4 & 32.7 & 40.4 & 21.4 & & & \end{array}\) c. The accompanying data are from a graph that appeared in the paper "Ladies First? A Field Study of Discrimination in Coffee Shops" (Applied Economics [April, 2008]). The data are the wait times (in seconds) between orderingand receiving coffee for 19 female customers at a Boston coffee shop. \(\begin{array}{lrrrrrr}60 & 80 & 80 & 100 & 100 & 100 & 120 \\ 120 & 120 & 140 & 140 & 150 & 160 & 180 \\ 200 & 200 & 220 & 240 & 380 & & \end{array}\)

Short answer

For Dataset A, use median as the measure of center and interquartile range for spread. For Dataset B, use mean for measure of center and standard deviation for spread. For Dataset C, use median as the measure of center and interquartile range for spread.

Step-by-step solution

Analyze Dataset A

For this dataset, to describe the center, compute the median of the data points as there are observable outliers i.e., multiple zero values which would impact the mean significantly and may not provide an accurate measure of center. Compute the interquartile range to measure the spread as it provides a better set of values considering the dataset's structure.

Analyze Dataset B

The dataset may have some outliers (e.g., 73.0 and 73.5), but overall the distribution seems fairly regular. Hence, the mean can be computed to represent the data's center. The standard deviation can be used to measure the spread as it provides an understanding of the variation in the amount of alcohol poured.

Analyze Dataset C

Looking at the data, it seems that there is a wide disparity in wait times, with some values significantly higher than others (e.g., 380). Therefore, it would be more appropriate to use the median as the measure of center and the interquartile range for spread as it mitigates the impact of extreme values.