Kurtosis is another measure of the shape of a frequency curve. It is a Greek word, which means bulginess. While skewness signifies the extent of asymmetry, kurtosis measures the degree of peakedness of a frequency distribution. Karl Pearson classified curves into three types on the basis of the shape of their peaks. These are mesokurtic, leptokurtic and platykurtic. These three types of curves are shown in figure below:

It will be seen from Figure that mesokurtic curve is neither too much flattened nor too much peaked. In fact, this is the frequency curve of a normal distribution.      

Leptokurtic curve is a more peaked than the normal curve. In contrast, platykurtic is a relatively flat curve. The coefficient of kurtosis as given by Karl Pearson is b2=m4/m22. In case of a normal distribution, that is, mesokurtic curve, the value of b2=3. If b2 turn out to be > 3, the curve is called a leptokurtic curve and is more peaked than the normal curve. Again, when b2 < 3, the curve is called a platykurtic curve and is less peaked than the normal curve.

The measure of kurtosis is very helpful in the selection of an appropriate average. For example, for normal distribution, mean is most appropriate; for a leptokurtic distribution, median is most appropriate; and for platykurtic distribution, the quartile range is most appropriate

.

Example 1: From the data given in Example 3.18, calculate the kurtosis.

Where K = kurtosis, Q = ½ (Q3 – Q1) is the semi-interquartile range; P90 is 90th percentile and P10 is the 10th percentile. This is also known as the percentile coefficient of kurtosis. In case of the normal distribution, the value of K is 0.263.

Example 2: From the data given below, calculate the percentile coefficient of kurtosis.

Daily Wages in Rs.

Number of Workers

cf

50- 60

10

10

60-70

14

24

70-80

18

42

80 - 90

24

66

90-100

16

82

100 -110

12

94

110 - 120

6

100

Total

100

 

It will be seen that the above distribution is very close to normal distribution as the value of K is 0.268, which is extremely close to 0.263.