031. Skewness and Coefficient of Variation

Not all distributions are normal. Some are skewed left (Fig.3.5a) or right (Fig.3.5b). In Figure 3.5, distribution curves for people’s weights can be found.

A B

Figure 3.5 – Skewed Distribution of People’s Weights:

A – Distribution skewed to the left; B - Distribution skewed to the right

In both cases in Figure 3.5, the mode is, by definition, that observation occurring with the greatest frequency. It is therefore at the peak of the distribution. The mean is most affected by extreme observations. Therefore it is pulled in the direction of skewness more than is the median, which lies between the mean and the mode. These conditions of skewness are significant and can be measured by the Pearsonian coefficient of skewness.

. (3.20)

If P<0, the data are skewed left; if P>0, the are skewed right; if P = 0, they are normally distributed.

The Coefficient of variation Serves as a relative measure of dispersion. The coefficient of variation assesses the degree of dispersion of a data set relative to its mean.

. (3.21)

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