The Standard Deviation

The standard deviation concept was introduced by Karl Pearson in 1893. It is by far the most important and widely used measure of studying dispersion. Its significance lies in the fact that it is free from those defects from which the earlier methods suffer and satisfies most of the properties of a good measure of dispersion. Standard deviation is also known as root-mean square deviation for the reason that it is square root of the means of the squared deviations from the arithmetic mean. Standard deviation is denoted by the small Greek letter σ (read as sigma).

The standard deviation measures the absolute dispersion or variability of a distribution; the greater the amount of dispersion or variability the greater the standard deviation, for the greater will be the magnitude of the deviations of the values fro their mean. A small standard deviation means a high degree of uniformity of the observations as well as homogeneity of a series; a large standard deviation means just the opposite. Thus if we have two or more comparable series with identical or nearly identical means, it is the distributions with the smallest standard deviation that has the most representative mean. Hence standard deviation is extremely useful in judging the representativeness of the mean.

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