easiest way to approach the subject of summary statistics
is to focus on what we have and what we want to achieve:
- We have a set of observations which we want to summarize.
- 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
There are other alternatives, of course. The median
, 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.
back to statistical theory -- summarizing statistical data