Q.13. Explain variance and coefficient of variation.(2013-14)
Ans. The square of the standard deviation is called variance. Therefore, Variance = 02. It is comparable with standard deviations and greater the standard deviation, greater the variability. For grouped data,
Ef(x – X)
Standard deviation a = Ef(x – x)2/n
A frequently used relative measure of variation is the coefficient of variation denoted by C.V. This measure is simply the ratio of the standard deviation to mean expressed as the percentage. So, it is the percentage variation in mean, standard deviation being considered as the total variation in the mean. Thus, it shows relationship between the standard deviation and the arithmetic mean.
Coefficient of variation C.V.= x 100
When the coefficient of variation is less in the data, it is said to be less variable or more consistent.