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Variance

March 29, 2018

Variance.  The variance of a set of numbers, xnn = 1, …, N, with a known mean value of μ, is given by

equation3

If the mean value has been estimated from the set of numbers using Eq. 1, then the variance is given by

equation4

The value in the denominator before the summation is the number of independent values used (or degrees of freedom) in the summation. Since x  has been computed from the same set of numbers as used in Eq. 4, the value of the last term in the summation in Eq. 4 is predetermined, so the number of independent values in the summation is N – 1.

For a vibration signal with a mean value of zero, the variance is equal to the mean-square value. In general,

equation5

When summing independent random variables, the variances add (even with non-zero means).