Question

The coefficient of variations of two series are $58$ and $69$. Their standard deviations are $21.2$ and $15.6$. What are their arithmetic means?

Answer 1

We know that coefficient of variation, C.V. $=\frac{\sigma }{\overline{x}}\times 100$.
$\therefore \overline{x}=\frac{\sigma }{C.V}\times 100$.

Mean of the first series, $\overline{x_1}=\frac{\sigma }{C.V}\times 100$
$=\frac{21.2}{58}\times 100$ $\because C.V=58$ and $\sigma =21.2$

$=\frac{2120}{58}=36.6$
Mean of the second series, $\overline{x_2}=\frac{\sigma }{C.V}\times 100$

$=\frac{15.6}{69}\times 100$ $\because C.V=69$ and $\sigma =15.6$

$=\frac{1560}{69}$

$=22.6$
A.M of the I series $=36.6$ and the A.M of the II series $=22.6$.