Choosing summary statistics
Summary statistics are needed when we have a set of observations which we want to summarize, and we want to communicate as much as possible as simply as possible. Statisticians commonly try to describe the observations in
- a measure of location, or central tendency, like the arithmetic mean
- a measure of statistical dispersion like the standard deviation
- a measure of the shape of the distribution like skewness or kurtosis
The median, mode, and interquartile mean are also 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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