A Complete Guide to the Futures Market, 2nd Edition

Appendix B

A Review of Elementary Statistics

The theory of probabilities is at bottom nothing but common sense reduced to Calculus.

—Pierre Simon de Laplace

■ Measures of Dispersion

For any data series there are two basic types of descriptive statistics: (1) some measure of central tendency (e.g., arithmetic mean, median, mode, geometric mean, harmonic mean); and (2) a measure of dispersion. The intuitive meaning of dispersion is quite clear. For example, consider the following two sets of numbers:

1. 30, 53, 3, 22, 16, 104, 71, 41
2. 42, 40, 42, 46, 39, 45, 42, 44

Although both series have the same arithmetic mean, it is clear that series A would have a high dispersion measure and series B a low dispersion measure. The concept of dispersion is extremely important in forecasting. For example, if we were told there was a ninth number in each of the series that was not listed, we would be far more certain about our guess being close to the mark in series B than in series A. Thus, it is extremely desirable to have a measure that describes the dispersion of a set of numbers, much as the mean describes the central tendency of a set of numbers.

The basic question is: How do we measure dispersion? In a sense, we have already answered this question. Deriving a dispersion measure for a set of numbers is entirely analogous to the computation of a single deviation measure for a group of points from a line. In the case of a set of numbers, the deviations would be measured relative to some ...