The following results show the number of workers and the wages paid to them in two factories A and B of the same industry.
The following results show the number of workers and the wages paid to them in two factories A and B of the same industry.
(i) Which firm pays a larger amount as monthly wages?
(ii) Which firm shows greater variability in individual wages?
(i) Both the factories pay the same mean monthly wages.
For factory A there are 560 workers. And for factory B there are 650 workers.
So, factory A totally pays as monthly wage $=(5460 \times 560)$ Rs. $=3057600 \mathrm{Rs}$.
Factory B totally pays as monthly wage $=(5460 \times 650)$ Rs. $=3549000 \mathrm{Rs}$.
That means, factory B pays a larger amount as monthly wages.
(ii) Mean wages of both the factories are the same, i.e., Rs. 5460 .
To compare variation, we need to find out the coefficient of variation (CV).
We know, CV = $\frac{\mathrm{SD}}{\text { Mean }} \times 100$ where SD is the standard deviation.
The variance of factory $A$ is 100 and the variance of factory $B$ is 121 .
Now, SD of factory A =
$\sqrt{100}=10$
And, SD of factory B =
$\sqrt{121}=11$
Therefore,
The $C V$ of factory $A=$
$\frac{10}{5460} \times 100=.183$
The $\mathrm{CV}$ of factory $\mathrm{B}=$
$\frac{11}{5460} \times 100=.201$
Here, the $C V$ of factory $B$ is greater than the $C V$ of factory $A$.
Hence, factory B shows greater variability.