The average and measure of
dispersion can describe the distribution but they are not sufficient to
describe the nature of the distribution. For this purpose we use other concepts
known as Skewness and Kurtosis. The symmetrical and skewed distributions are shown by curves as

**Skewness**

Skewness means lack of
symmetry. A distribution is said to be symmetrical when the values are
uniformly distributed around the mean. For example, the following distribution
is symmetrical about its mean 3.

x : 1 2
3 4 5

frequency (f ) : 5 9 12 9 5

In a symmetrical
distribution the mean, median and mode coincide, that is, mean = median = mode.

Several measures are used to
express the direction and extent of skewness of a dispersion. The important
measures are that given by Pearson. The first one is the Coefficient of
Skewness:

For a symmetric distribution

*S*= 0. If the distribution is negatively skewed then_{k}*S*is negative and if it is positively skewed then_{k}*S*is positive. The range for_{k}*S*is from -3 to 3._{k}
The other measure uses the

*b*(read ‘beta’) coefficient which is given by, where, m_{2}and m_{3}are the second and third central moments. The second central moment m_{2 }is nothing but the variance. The sample estimate of this coefficient is where m_{2}and m_{3}are the sample central moments given by
For a symmetrical
distribution b

_{1}= 0. Skewness is positive or negative depending upon whether m_{3}is positive or negative.**Kurtosis**

A measure of the peakness or convexity of a
curve is known as Kurtosis.

It is clear from the above figure that all
the three curves, (1), (2) and (3) are symmetrical about the mean. Still they
are not of the same type. One has different peak as compared to that of others.
Curve (1) is known as mesokurtic (normal curve); Curve (2) is known as leptocurtic (leading curve) and
Curve (3) is known as platykurtic (flat curve). Kurtosis is measured by Pearson’s
coefficient, b

The sample estimate of this coefficient is where, m

_{2}(read ‘beta - two’).It is given by .The sample estimate of this coefficient is where, m

_{4}is the fourth central moment given by m_{4}=
The distribution is called normal if b

_{2}= 3. When b_{2}is more than 3 the distribution is said to be leptokurtic. If b_{2}is less than 3 the distribution is said to be platykurtic.