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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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    $\begingroup$ There's some potential confusion due to a strange use of "from." When we compute something from something else, we are using the something else in our computation. However, you don't seem to be asking about computing variances or SDs from a mean: you seem to be asking about computing them for a mean. "For" means that the variance or SD is computed from a random sample and that it is intended to estimate some property of the population being sampled. To that we can understand what you need, could you please rephrase your question using these conventional senses of "for" and "from"? $\endgroup$
    – whuber ♦
    Nov 19, 2012 at 19:59
  • $\begingroup$ You're not looking for the standard error, are you? $\endgroup$
    – ahans
    Nov 19, 2012 at 20:00
  • $\begingroup$ Isn't it a standard result in probability theory that $$E[(X-a)^2] = E[(X-\mu)^2] + (\mu-a)^2 = \sigma^2 + (\mu-a)^2,$$ that is, the mean-square deviation from $a$ equals the sum of the variance and the square of the distance between $\mu$ and$a$? This used to be called the theorem of parallel axes in mechanics: the moment of inertia about any axis parallel to the axis through the center of mass is the central moment of inertia plus the moment about the new axis of the entire mass regarded as a point mass situated at the center of mass? $\endgroup$
    – Dilip Sarwate
    Nov 20, 2012 at 23:59

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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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