### Sample estimators of distribution moments

Sample moments are calculated using the observed values *x*_{1}, *x*_{2}, ..., *x*_{n} of the variable *X*. Sample moments about the origin are:

and sample moments about the mean are:

The sample estimate of the mean is the sample moment *m*'_{1}, which is actually the arithmetic mean, or the average, of the sample values:

Sample moments *m*_{2} and *m*_{3} are not usually used to estimate distribution moments because they can be biased. Instead, so called *unbiased estimators* are used:

where *s* is the usual notation for sample standard deviation. Coefficients of variation and skewness are then estimated with: