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Algorithms for calculating variance - Wikipedia

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Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values. A formula for calculating the variance of an entire population of size N is: Using Bessel's correction to calculate an unbiased estimate of the population variance from a finite sample of n observations, the formula is: Therefore, a naïve algorithm to calculate the estimated variance is given by the following: This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation. Thus thi

Algorithms for calculating variance - Wikipedia Jump to content From Wikipedia, the free encyclopedia Important algorithms in numerical statistics Algorithms for calculating variance play a major role in computational statistics . A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values. Naïve algorithm [ edit ] A formula for calculating the variance of an entire population of size N is: σ 2 = ( x − x ¯ ) 2 ¯ = ( x 2 )

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