**Moment Statistics**

Moments are a set of statistical parameters to measure a distribution. Four moments are commonly used:

- 1st, Mean: the average
- 2d, Variance:
- Standard deviation is the square root of the variance: an indication of how closely the values are spread about the mean. A small standard deviation means the values are all similar. If the distribution is normal, 63% of the values will be within 1 standard deviation.

- 3d, Skewness: measure the asymmetry of a distribution
about its peak; it is a number that describes the shape
of the distribution.
- It is often approximated by Skew = (Mean - Median) / (Std dev).
- If skewness is positive, the mean is bigger than the median and the distribution has a large tail of high values.
- If skewness is negative, the mean is smaller than the median and the distribution has a large tail of small values.

- 4th: Kurtosis: measures the peakedness or flatness of a
distribution.
- Positive kurtosis indicates a thin pointed distribution.
- Negative kurtosis indicates a broad flat distribution.

Higher moments tend to be less robust. Press and others (1986, p.457) recommend that skewness and kurtosis be used "with caution or, better yet, not at all".

*Last revision 8/6/2009*