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In statistics, sometimes we use mean sum of error, and sometimes variance. I just want to know what is the difference between mean sum of error and variance?

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    $\begingroup$ "MSE" stands for Mean Squared Error, not "mean sum of error." $\endgroup$ – gung Aug 8 '15 at 17:08
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$MSE = {\rm variance} + {\rm bias}^2$. As per gung, MSE is mean squared error.

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They measure two different things.

Variance measures the spread of a variable. While MSE measures the deviation from a predictor. MSE is usually associated with a function:

If you are trying to measure how well a function, say Y=mX+b, predicts Y then you would use MSE. Note that here the MSE <> Variance.

I could guess the confusion mostly comes from when you have a target value in manufacturing. Say you have a target value of 4 on a measurement. MSE would take into account the mean's shift from the target as well as the variance. So values of 2, 3, 4, 5 would yield MSE of 1.5 and variance of 1.3

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