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Updating mean and variance estimates an improved method

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However, the results of both of these simple algorithms (“Naïve” and “Two-pass”) can depend inordinately on the ordering of the data and can give poor results for very large data sets due to repeated roundoff error in the accumulation of the sums.Techniques such as compensated summation can be used to combat this error to a degree.Yet, it is more expensive to compute than primary measures such as SUM, MEAN, and COUNT.There exist numerous techniques to compute variance.This is particularly bad if the standard deviation is small relative to the mean.However, the algorithm can be improved by adopting the method of the assumed mean.

updating mean and variance estimates an improved method-7

Thus this algorithm should not be used in practice.To ensure the availability of the Digital Library we can not allow these types of requests to continue.The restriction will be removed automatically once this activity stops. Then the in all three updates the summation may sum quantities of very different magnitude, leading to large round-off errors.By the way, this can even arise when one is computing the simple sum of many numbers, and a classic solution in that case is Kahan summation.Variance is a popular and often necessary component of aggregation queries.