Summary statistics

The easiest way to approach the subject of summary statistics is to focus on what we have and what we want to achieve:

1. We have a set of observations which we want to summarize.
2. We want to communicate as much as possible as simply as possible.

Statisticians commonly try to describe the observations in

1. a measure of location, or central tendency, like the arithmetic mean
2. a measure of statistical dispersion like the standard deviation
3. a measure of the shape of the distribution like skewness or kurtosis

There are other alternatives, of course. The median, mode, and interquartile mean are both measures of location. To describe the statistical dispersion, we can use the statistical range, the interquartile range, or the absolute deviation.

The Gini coefficient was originally developed to measure income inequality, but can be used for other purposes as well.

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