Measures of distribution shape

Measure	Definition	Expression(s)
Skewness, α₃	If a frequency distribution is unimodal and symmetric about the mean it has a skewness of 0. Values greater than 0 suggest skewness of a unimodal distribution to the right, whilst values less than 0 indicate skewness to the left. A function of the 3^rd moment about the mean (denoted by α₃ with a ^ symbol above it for the sample skewness)
Kurtosis, α₄	A measure of the peakedness of a frequency distribution. More pointy distributions tend to have high kurtosis values. A function of the 4^th moment about the mean. It is customary to subtract 3 from the raw kurtosis value (which is the kurtosis of the Normal distribution) to give a figure relative to the Normal (denoted by α₄ with a ^ symbol above it for the sample kurtosis)	where ,

Measure

Definition

Expression(s)

Skewness, α₃

If a frequency distribution is unimodal and symmetric about the mean it has a skewness of 0. Values greater than 0 suggest skewness of a unimodal distribution to the right, whilst values less than 0 indicate skewness to the left. A function of the 3^rd moment about the mean (denoted by α₃ with a ^ symbol above it for the sample skewness)

Kurtosis, α₄

A measure of the peakedness of a frequency distribution. More pointy distributions tend to have high kurtosis values. A function of the 4^th moment about the mean. It is customary to subtract 3 from the raw kurtosis value (which is the kurtosis of the Normal distribution) to give a figure relative to the Normal (denoted by α₄ with a ^ symbol above it for the sample kurtosis)

where