Kurtosis

Kurtosis is also quite simple to visualize. It essentially measures the degree to which data is concentrated closer to the mean versus further from it. In other words, from a visual point of view, is the data concentrated closer to the hump in the curve or further toward the tails.

Kurtosis comes in three types.

1. Mesoteric

This is closer to the ideal bell curve. We have seen this in the bell curve example earlier. The data is evenly distributed with a moderate breadth and medium height peak. Kurtosis is closer to a value of 3 in this case.

See the chart for an example.

2. Platykurtic

When the Kurtosis value is less than 3, it indicates a case where the data is concentrated in the center, closer to the mean. The curve looks shorter (or flatter) with longer tails. In fact, the curve is deformed to the extent that it's hard to draw a line between the peak and the tails.

See below for an example.

3. Leptokurtic

Lastly, when the Kurtosis value is greater than 3, it tells us that the data is concentrated in the tails, further from the mean. The curve looks sharply tall with thick tails. The curve shows distinct peaks and tails.

See below for an example.

A practical use for Kurtosis can be found in the area of investment management. A leptokurtic curve for the returns of an asset indicates the presence of high risk. Either the asset returns very high or very low, indicating the presence of high risk.