. Coefficient of Variation Comparison of two data in terms of measures of central tendencies and dispersions in some cases will not be meaningful, because the variables in the data may not have same units of measurement. For example consider the two data Weight Price Mean kg ₹ Standard deviation . kg ₹ .
Here we cannot compare the standard deviations . kg and ₹ . . For comparing two or more data for corresponding changes the relative measure of standard deviation, called “ Coefficient of variation ” is used.
Coefficient of variation of a data is obtained by dividing the standard deviation by the arithmetic mean. It is usually expressed in terms of percentage. This concept is suggested by one of the most prominent Statistician Karl Pearson . Thus, coefficient of variation of first data (C.V ) = s % coefficient of variation of second data (C.V ) = s % The data with lesser coefficient of variation is more consistent or stable than the other data.
Consider the two data Mean Standard deviation . . If we compare the mean and standard deviation of the two data, we think that the two datas are entirely different. But mean and standard deviation of B are % of that of A .
Because of the smaller mean the smaller standard deviation led to the misinterpretation. Statistics and Probability To compare the dispersion of two data, coefficient of variation = s % The coefficient of variation of A = % . % The coefficient of variation of B = % . % Thus the two data have equal coefficient of variation.
Since the data have equal coefficient of variation values, we can conclude that one data depends on the other. But the data values of B are exactly %