Question

The mean of a distribution is 4. If its coefficient of variation is 58%. Then the S.D of the distribution is
$(a){\text{ 2}}{\text{.23}} \\\ (b){\text{ 3}}{\text{.23}} \\\ (c){\text{ 2}}{\text{.32}} \\\ (d){\text{ none of these}} \\\$

Answer 1

Hint – In this question use the direct formula for coefficient of variation which is ratio of standard of deviation and the mean, that is $C.V = \dfrac{{S.D}}{\mu }$, to find the standard deviation.
Complete step-by-step answer:
Given data
Mean of a distribution ($\mu$) = 4.
Coefficient of variation (C.V) = 58%.
Now as we know that coefficient of variation is the ratio of standard deviation (S.D) to mean.
Therefore, C.V = $\dfrac{{S.D}}{\mu }$
Now substitute the values we have,
$\Rightarrow \dfrac{{58}}{{100}} = \dfrac{{S.D}}{4}$
Now simplify the above equation we have,
$\Rightarrow S.D = \dfrac{{58 \times 4}}{{100}} = \dfrac{{58}}{{25}} = 2.32$
So this is the required answer.
Hence option (C) is correct.
Note – It’s important to understand the physical significance of standard deviation, mean and coefficient of variation. Standard deviation expresses the quantity that by how much the members of a group differ from the mean value of the group. Mean is the average of the numbers and it is defined as the ratio of summation of all the numbers divided by the total numbers. Coefficient of variation determines the greatness of the level of dispersion around the mean.