comparing the variability or dispersion of two series, we calculate the coefficient of variance for each series. The series having greater C.V. is said to be more variable than the other. The series having lesser C.V.
is said to be more consistent than the other. STATISTICS . . Comparison of two frequency distributions with same mean Let x and σ be the mean and standard deviation of the first distribution, and x and σ be the mean and standard deviation of the second distribution.
Then C.V. (1st distribution) = σ × and C.V. (2nd distribution) = σ × Given x = x = x (say) Therefore C.V. (1st distribution) = σ × ...
( ) and C.V. (2nd distribution) = σ × ... ( ) It is clear from ( ) and ( ) that the two C.Vs. can be compared on the basis of values of σ and σ only.
Thus, we say that for two series with equal means, the series with greater standard deviation (or variance) is called more variable or dispersed than the other. Also, the series with lesser value of standard deviation (or variance) is said to be more consistent than the other. Let us now take following examples: Example Two plants A and B of a factory show following results about the number of workers and the wages paid to them. A B No.
of workers Average monthly wages Rs Rs Variance of distribution of wages In which plant, A or B is there greater variability in individual wages? Solution The variance of the distribution of wages in plant A ( σ ) = Therefore, standard deviation of the distribution of wages in plant A ( σ ) = MATHEMATICS Also, the variance of the distribution of wages in plant B ( σ ) = Therefore, standard deviation of the distribution of wages in plant B ( σ ) = Since the average monthly wages in both the plants is same, i.e., Rs. , therefore, the plant