# Kurtosis

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Just like Skewness, Kurtosis is also used to measure the deviation in data from normal distribution. Kurtosis is a measure of the degree to which a distribution is more or less “peaked” than the normal distribution.

Kurtosis can be divided into three categories:

Leptokurtic:  Leptokurtic describes a distribution that is more peaked than a normal distribution. A leptokurtic distribution will have more data points clustered around the mean and more data points with large deviations from the mean (fatter tails). Relative to a normal distribution, a leptokurtic distribution will have a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the mean.

Platykurtic: Platykurtic describes a statistical distribution with thinner tails than a normal distribution. Because this distribution has thin tails, it has fewer outliers (e.g., extreme values three or more standard deviations from the mean) than do mesokurtic and leptokurtic distributions.

Mesokurtic: A distribution is mesokurtic if it has the same kurtosis as a normal distribution.

To interpret kurtosis, note that it is measured relative to the kurtosis of a normal distribution, which is 3. Positive values of excess kurtosis indicate a distribution that is leptokurtic (more peaked, fat tails), whereas negative values indicate a platykurtic distribution (less peaked, thin tails). Excess kurtosis values that exceed 1.0 in absolute value are considered large. We can calculate kurtosis relative to that of a normal distribution as:

excess kurtosis = sample kurtosis – 3