Students are introduced to statistics, which summarize qualities of a distribution, by inventing a measure of the “real” height of the flagpole, given the data they have collected. (Or, perhaps one of the measurement data sets that accompany the unit). The measure is a statistic corresponding to the central tendency of the data. In the context of measurement, center corresponds to “best guess” or true value of the measurement. The idea is that an object has a true length or mass or area, etc., and the center of the distribution of measures is our best estimate of this true value. Traditionally, we employ the mean (which takes a “per” case view of the data by taking the ratio of the sum to the total number of cases), median (which represents a middle of the data by selecting the value splitting the data into 2 parts of equal number when the values are ordered from least to greatest), or mode (which takes the view that the most frequent value is often most representative). However, students may invent other measures as well, and they should be encouraged to do so. The pedagogical intention is to help students come to understand the function of a statistic-to summarize an attribute of a distribution—and to understand what might be meant by the attribute of center (of a distribution). Some of these intentions are realized by having students invent measures, but others are realized as students compare and contrast different methods. The lesson concludes with a discussion of the relation between the process of measure and the methods developed to summarize the “best guess” of the true height of the flagpole.
