ABSTRACT
At the end of Chapter 3, we stated that by itself, a measure of central tendency is not sufficient to describe a set of data fully and properly. The reason for this is that such measures focus attention on only one aspect of the data, centrality, and in doing so suppress any information that shows the extent to which the data depart from centrality. An example should help to illustrate the importance of describing data by providing information about both centrality and dispersion. Consider the following sets of data:
A: 93, 93, 93, 93, 93 B: 92,93,93,93,94 C: 91,92,93,94,95 D: 89,91,93,95,97 E: 73,83,93, 103,113
For each of these sets the mean (and median) is 93. If all we knew about the data sets was these average scores, we might readily conclude that the five groups were quite similar, if not identical. But clearly the groups are not identical, and not even similar in the more extreme comparisons (such as A vs. E). In group A, each score is identical to every other score; the chosen average is perfectly representative of the entire set; there is no deviation from centrality, no dispersion. In B, there is some variation in scores, but the mean (or median) is still quite representative; the amount of dispersion is slight. But in D, and especially in E, the scores diverge from each other and from the mean to a marked degree, and in these instances we can begin to question seriously how representative our average scores
really are. From these simple examples we can see that we need more than a measure of centrality if we wish to describe a set of data fully and properly.
