Used in statistics, kurtosis is a way of measuring the deviation of a distribution from the normal distribution, just like variance or skewness. In fact, the method of calculating kurtosis is similar to the method of calculating skewness and variance.

Kurtosis is calculated as the average of the fourth power of the distribution's deviation from the mean, divided by the standard deviation to the fourth power. Finally, a correction of 3 is subtracted, so that the kurtosis of a normal distribution is zero.

Graphically, kurtosis measures the relative size of a distribution's outlying sections. These are sometimes referred to as tails, and are the regions on each side of the main part of the distribution, where the probability trails off to zero. A distribution with a positive kurtosis is called leptokurtic, and has large tails. The opposite, a distribution with negative kurtosis, is called platykurtic and has little to no tails at all. As the kurtosis approaches zero, the distribution is mesokurtic, and approaches a normal distribution sort of shape.

A leptokurtic and a platykurtic distribution could share identical variances, skews, and means, even though the kurtosis is opposite in sign.

For example:

Imagine going to a high school cafeteria during lunchtime. If you were to survey the age of each person eating in this cafeteria, you would get ages in a very specific range, with few outliers. This is an example of a platykurtic distribution.

Conducting the same study at a restaurant like Applebee's during early dinnertime, when parents bring their children, and when more older folks are present, would result in an age distribution curve that has more outliers. It is very probable that this distribution would be leptokurtic. It is certain that the kurtosis would be more positive here than in the first case.

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