The Standard Deviation: Some Drawbacks of an Intuitive Approach

In a recent issue of this journal, Hart [2] mentioned that "she made a habit of asking students of all levels what a standard deviation is". She complained that in most students the only answer was: "It's a measure of spread", upon which they provide a formula. We are still more pessimistic. We doubt whether most students do realize that the standard deviation is a special measure of spread: one that measures how strongly the data depart from central tendency. Our doubt has been induced by the way in which many textbooks introduce the concept of variability. Most introductions put a stronger emphasis on the heterogeneity among the observations than on their deviations from the central tendency. An example may illustrate our point.