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Required Statistics:

**Standard Deviation**

Consider a population consisting of the following eight values:

These eight data points have the mean (average) of 5:

To calculate the population standard deviation, first compute the difference of each data point from the mean, and square the result of each:

Next compute the average of these values, and take the square root:

**Mean Squared Error**

See
Mean Squared Error on Wikipedia

**Absolute Error**

Given some value *v* and its approximation *v*_{approx}, the
**absolute error** is

where the vertical bars denote the
absolute value. If the
**relative error** is

**Relative Error**

and the **percent error** is

These definitions can be extended to the case when *v* and
*v*_{approx} are
*n*-dimensional vectors, by replacing the absolute value with an
*n*-norm.^{[1]}

References:

Approximation Error

Standard Deviation

Mean Squared Error on Wikipedia

Last edited Apr 18, 2011 at 12:33 AM by sesmar, version 1