Is there a term(s) for calculating the variance or standard deviation from a value other than the mean?

**Example:**

If I have a set of estimates for jelly beans in a jar, calculating standard deviation and variance is an operation on the mean of those estimates. However, I also want to find the "standard deviation" of the distribution from the *actual* number of jelly beans in the jar. Is this still called **standard deviation** even though it's not the deviation from the mean? Is there a term or specific subject area for analysis of a distribution against an independent value like this?

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#### Best Answer

You are asking about the root mean squared error of the prediction. There is a Wikipedia entry for Mean squared prediction error, which is the analog for the variance. However, RMSEP will be more interpretable (just like the SD is). The calculation is just as you suspect, replacing the estimated sample mean with the true value. Note that RMSEP will include *both* the SD and the bias (the degree to which the sample mean deviates from the true value). Depending on what you want, it may be useful to keep those two numbers distinct.

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