Abstract
This chapter discusses variance, standard deviation, skewness, and kurtosis. There are essentially four approaches by which the variability of quantitative data may be characterized. The variability indicated by the difference between the smallest x-value, x-min and the largest x-value, x-max: L = x-max – x-min, is termed the range of the distribution. This simple approach to variability is used widely in the older paleontological literature. The number L is a measure of the distance between the tails of a distribution. The variance and its square root, the standard deviation or root mean square deviation, are the measures of variability that are used by the statistician. Both variance and mean deviation take into account all values of the distribution whereas the range reflects only the distance between the tails of a distribution. The coefficient α3 is zero only if the distribution is symmetrical. To some extent, skewness also is indicated by Pearson's first or second measure of skewness. The variance and its square root, the standard deviation or root mean square deviation, are the measures of variability that are used by the statistician.
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