Variance and Standard Deviation

Functions > Statistics > Descriptive Statistics > Variance and Standard Deviation

Variance and Standard Deviation

The following two functions return the variance and the standard deviation of a population, with the variance defined as follows:

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• var(A, B, C, ...)—Returns the population variance of the elements of A, B, C, ....

• stdev(A, B, C, ...)—Returns the square root of the population variance of the elements in A, B, C, ....

The following two functions return the variance and the standard deviation of a sample, with the variance defined as follows:

Click to copy this expression

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• Var(A, B, C, ...)—Returns the sample variance of the elements of A, B, C, ... .

• Stdev(A, B, C, ...)—Returns the square root of the sample variance of the elements in A, B, C, ....

The population variance and standard deviation are divided by t, the total number of values, rather than t – 1 for the sample variance and standard deviation. Dividing the squared deviations by the sample size minus one, rather than the sample size, provides a better estimate for the true population variance. The population and sample functions are distinguished by their capitalization, so use care when typing the function names.

Although the variance is intended to be an overall measure of the spread of a distribution, it is strongly affected by the tail behavior.

Arguments

• A, B, C, ... are scalars or m x n arrays.

• M is an array created from the function arguments A, B, C, ....