Summarizing a Large Quantity of Data: Statistics
The most important summary of a quantity of numerical data consists of the calculation of key numbers, called statistics, to describe its distribution. This chapter takes up the two most useful kinds of statistics: measures of central tendency and dispersion.
A statistic of central tendency, often called an average, is a single number used to represent the general magnitude of all items in a distribution. It is "typical" of the observed magnitudes. Three averages are in general use: the mode, the median, and the arithmetic mean. While these averages have important properties in common, they differ in many respects and involve different definitions of what is "typical." In selecting the average theoretically appropriate to any particular purpose this definition is the controlling factor.
The mode is the point in a frequency distribution at which the frequency density reaches a maximum. It takes as "typical" that value which occurs more frequently than any other single magnitude. The mode is, in a sense, the most "popular" value in the frequency distribution, and is clearly the average to use to express, say, the "typical" length of women's dresses. Indeed, the term "mode" is derived from the French word for "fashion." As a point of maximum density, the mode is sometimes used in the study of traffic congestion and peak loads on