In statistics, the concept of the shape of the distribution refers to the shape of a probability distribution and it most often arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms such as "J-shaped", or numerically, using quantitative measures such as skewness and kurtosis.
Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes.
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“The man who pretends that the distribution of income in this country reflects the distribution of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”
—George Bernard Shaw (1856–1950)