standard deviation

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standard deviation

In statistics, a measure (symbol ςor s) of the spread of data. The deviation (difference) of each of the data items from the mean is found, and their values squared. The mean value of these squares is then calculated. The standard deviation is the square root of this mean.

If n is the number of items of data, x is the value of each item, and μ is the mean value, the standard deviation ςmay be given by the formula

where Σ indicates that the differences between the value of each item of data and the mean should be summed.

To simplify the calculations, the formula may be rearranged to

As a result, it becomes necessary only to calculate Σx and Σx².

For example, if the ages of a set of children were 4, 4.5, 5, 5.5, 6, 7, 9, and 11, Σx would be 52, μ would be 52/n = 52/8 = 6.5, and Σx² would be 378.5 (= 4² + 4.5² + 5² + 5.5² + 6² + 7² + 9² + 11²).

Therefore, the standard deviation ςwould be

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