Statistics - Kurtosis

Kurtosis is a greek word which means “bulginess”. It is a statistical method that measure the shape of a frequency curve.Skewness measures the symmetricity of a curve however kurtosis measures the degree of peakedness.

On the basis of peakedness , Karl Pearson divided the curves into three types :-

• mesokurtic
• leptokurtic
• platykurtic

In the graph , we can see that the mesokurtic is neither flattened nor bulged .It is similar to normal distribution.

Leptokurtic is more peaked while Platykurtic is flattened one.

The kurtosis is very helpful in determining the appropriate average .

For normal distribution , mean is most appropriate , for a lepto median is most appropriate while for platy the quartile range is the best.

Kurtosis is helpful in finding the outliers availability in the data.

The coefficient of kurtosis as given by Karl Pearson is β 2 = μ 4 / μ 22 . In case of a normal distribution, that is, mesokurtic curve, the value of β 2 =3. If β 2 turn out to be > 3, the curve is called a leptokurtic curve and is more peaked than the normal curve. Again, when β 2 < 3, the curve is called a platykurtic curve and is less peaked than the normal curve.