with greater standard deviation will have more variability. Thus, the plant B has greater variability in the individual wages. Example Coefficient of variation of two distributions are and , and their standard deviations are and , respectively. What are their arithmetic means.
Solution Given C.V. (1st distribution) = , σ = C.V. (2nd distribution) = , σ = Let x and x be the means of 1st and 2nd distribution, respectively. Then C.V.
(1st distribution) = σ × Therefore = or × × and C.V. (2nd distribution) = σ × i.e. = or × × Example The following values are calculated in respect of heights and weights of the students of a section of Class XI : Height Weight Mean . cm .
kg Variance . cm . kg Can we say that the weights show greater variation than the heights? Solution To compare the variability, we have to calculate their coefficients of variation.
Given Variance of height = .69cm Therefore Standard deviation of height = .69cm = . cm Also Variance of weight = . kg STATISTICS Therefore Standard deviation of weight = kg = . kg Now, the coefficient of variations (C.V.) are given by (C.V.) in heights = Standard Deviation Mean × × = .
and (C.V.) in weights = × = . Clearly C.V. in weights is greater than the C.V. in heights Therefore, we can say that weights show more variability than heights.
EXERCISE . . From the data given below state which group is more variable, A or B? Marks - - - - - - - Group A Group B .
From the prices of shares X and Y below, find out which is more stable in value: X