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If a statistical data set is regularly distributed or skewed, the box plot shape will show it. The distribution is symmetric when the median is in the centre of the box and the whiskers on both sides are roughly the same.

A measure of kurtosis is a measure of the "tailedness" of a real-valued random variable's probability distribution in statistics. The standard kurtosis measurement is based on a scaled version of the data or population's fourth moment.

The Boxplot as a Tail Length Indicator:

  • The Normal population - the bell shaped curve - represents the ideal level of kurtosis, which is neither too heavy nor too light. A sample from a Normal population should have whiskers that are about the same length as the box, or slightly longer.

The histogram can give you an idea of the shape, but two numerical measures of shape can give you a more precise assessment: skewness and kurtosis. Skewness tells you the amount and direction of skew (departure from horizontal symmetry), while kurtosis tells you how tall and sharp the central peak is in comparison to a standard bell curve.

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