Summary statistics

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Box plot of the Michelson–Morley experiment, showing several summary statistics.

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible. Statisticians commonly try to describe the observations in

1. a measure of location, or central tendency, such as the arithmetic mean, median, mode, or interquartile mean
2. a measure of statistical dispersion like the standard deviation, variance, range, or interquartile range, or absolute deviation.
3. a measure of the shape of the distribution like skewness or kurtosis

A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.

Example

The following example using R is the standard summary statistics of a randomly sampled normal distribution, with a mean of 0, standard deviation of 1, and a population of 50:

> x <- rnorm(n=50, mean=0, sd=1)
> summary(x)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-1.72700 -0.49650 -0.05157  0.07981  0.67640  2.46700

Examples of summary statistics

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

See also

• descriptive statistics
• statistical theory
• sufficient statistic