Question

The Coefficient of variance of a distribution is $80\%$ and the mean of the distribution is $40$, the Standard Deviation of the distribution is?

Answer 1

Here we have to find out the standard deviation of the distribution.
So, we have to use the given data to find out by using the formula for coefficient of variance.
First we have to convert the data into decimal form.
Then we do some simplification and we get the required answer.

Formula used: ${\text{C}}{\text{.V = }}\dfrac{{{\sigma }}}{{{\mu }}}$, Where ${\text{C}}{\text{.V}}$ is the coefficient of Variance $\mu$ is the mean of the distribution and $\sigma$ is the Standard deviation.

Complete step-by-step solution:
It is given in the question stated as Mean $\mu = 40$ and,
Coefficient of Variance ${\text{C}}{{.V = 80\% }}$
Now we have to converting from Percentage to decimal we get,
${\text{C}}{\text{.V = }}\dfrac{{{\text{80}}}}{{{\text{100}}}}{\text{ = 0}}{\text{.8}}$
After that we have to use the formula for coefficient of variance,
${\text{C}}{\text{.V = }}\dfrac{{{\sigma }}}{{{\mu }}}$
Putting the values and we get,
$\Rightarrow 0.8 = \dfrac{\sigma }{{40}}$
On taking cross multiplication, we have to find out the value for standard deviation $\sigma$ we get:
$\Rightarrow \sigma = 0.8 \times 40$
Let us multiply the term we get,
$\Rightarrow \sigma = 32$
Hence we get the value of standard deviation.

$\therefore$ The Standard Deviation of a distribution with means $40$ and C.V. ${{80\% }}$ is $32$

Note: A place where the solution could go wrong is converting the coefficient from percentage to decimal, coefficient of variance is always measured in terms of percentage.
Remembering the formula of the relation between the Coefficient of Variation, mean and the standard deviation of a distribution.
Coefficient of Variance measures the degree of dispersion of the overall data around the mean; it is represented as the ratio of the standard deviation to the mean.