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Standard deviation

A data set or sample is reasonably described by where the data points are centered (central tendency), how much spread or dispersion there is among the data points, and its frequency distribution (i.e., the shape of its histogram). This information allows interpretations and further calculations to be made from the data. Where the data set approximates a normal (bell-shaped) distribution, the mean is the best measure of central tendency, although medians are better central tendency measures for other distributions. If the distribution is approximately normal, then the standard deviation (SD) indicates the dispersion of the data.

It might be expected that the estimate of dispersion would be based on the average of the deviations of each data point from the mean, ignoring whether the deviations were ...

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