Chapter 44: Mean and Median: Situation 38 From the MACMTL–CPTM Situations Project

The following task was given to students at the end of the year in an AP Statistics class.

Consider the box plots and five-number summaries¹ for two distributions, each of which is comprised of a finite number of data values (see Figure 44.1 and Figure 44.2). Which of the distributions (Data Set 1 or Data Set 2) has the greater mean?

One student’s approach to this problem was to construct what he thought were probability distributions for each data set and to compare the corresponding expected values to determine which data set had the greater mean. The student formed four intervals using the five-number summaries and calculated the midpoint of each interval (i.e., he defined the intervals as the four quarters of the distributions, with each quarter containing 25% of the values for the distribution). Using the midpoint of each interval as the X-value for that interval, he then calculated the weighted mean for each probability distribution (see Figure 44.3). After completing his calculations, the student responded that the second data set had the larger mean.