**Kurtosis** is a **measure of the peakedness** in a dataset. For an n-element set, kurtosis is given by the formula:

Kurtosis=\dfrac{\frac{1}{n}((x_1-\overline{x})^4+(x_2-\overline{x})^4+\ldots+(x_n-\overline{x})^4)}{(\frac{1}{n}((x_1-\overline{x})^2+(x_2-\overline{x})^2+\ldots+(x_n-\overline{x})^2)^2}-3

where `\overline{x}`

is the arithmetic mean.

Histograms with kurtosis `\approx{0}`

are called **mesokurtic**. This is similar to normal distribution.

Histograms with kurtosis **smaller than 0** are called **platykurtic**. The tail of such a histogram is rather short and thin, while the peak is comparatively low and broad. The word **platykurtic** comes from Greek: **platy** means **broad, flat**, while **kurtos** means **bulging**. Platykurtic histograms are therefore relatively flat.

Histograms with kurtosis **greater than 0** are called **leptokurtic**. The tails of such a histogram is long and fat, but the peak is usually tall and sharp. The word **leptokurtic** comes from Greek: **lepto** means **narrow**. Leptokurtic histograms are prominently peaked.

In case you're wondering, **meso** means **middle** in Greek, thus mesokurtic histograms are in the middle between platykurtic and mesokurtic histograms.