Question

if the mean of a series is 10 and its coefficient of variation is 40 % the variance of the series is what​

Answer 1

Variance of Series is 16.

Step-by-step explanation:

We are given that the mean of a series is 10 and its coefficient of variation is 40%.

And we have to find the variance of the series.

Firstly, Coefficient of variation formula is given by;

     Coefficient of Variation (C.V.) = $\frac{\text{Standard Deviation}}{\text{Mean}} \times 100$

In question we are provided with C.V. = 40% and Mean of series = 10

So,        C.V.  =  $\frac{\text{Standard Deviation}}{\text{Mean}} \times 100$

               40  =  $\frac{\text{Standard deviation}}{10} \times 100$

           Standard Deviation = $\frac{40 \times 10}{100}$

                                             = $\frac{400}{100} = 4$

So, Standard deviation of the series is 4. But we have to find the variance of series.

Hence, Variance is given by = $(\text{Stanadard deviation})^{2}$

                                                = $4^{2} =16$

Therefore, the variance of the series is 16.