Question

An anaoysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:

$\begin{array}{ccc}& \text{Firm A}& \text{Firm B}\\ \text{Average weekly wages}& 586& 648\\ \text{Average weekly wages}& Rs.52.5& Rs.47.5\\ \text{Variance of the distribution of wages}& 100& 121\end{array}$

(i) Which firm A or B pays out larger amount as weekly wages ?

(ii) Which firm A or B has greater variability in individual wages ?

Answer 1

(i) Total wages paid by firm A = (Average wages ) $\times$ (Number of employees) $52.5\times 587=Rs.30817.50$

Total wages paid by firm B = (Average wages) $\times$ (Number of employees) = $47.5\times 648=Rs.30780$

So, firm A pays higher total wages.

(ii) In order to compare the variability of wages among the two firms, we have to calculate their coefficient of variation.

Let ${\sigma }_1$ and ${\sigma }_2$ denote the standard deviations of Firm A and Firm B respectively. Further,

Let $\overline{X_1}$ and $\overline{X_2}$ be the mean wages in forms A and B respectively.

We have $\overline{X}=52.5,\overline{X_2}=47.5$

${\sigma }_1^2=100$ and ${\sigma }_2^2=121$

$\Rightarrow {\sigma }_1=\sqrt{100}=10$ and ${\sigma }_2=\sqrt{121}=11$

Now,

Coefficient of variation in wages in firm A$=\frac{{\sigma }_1}{\overline{X_1}}\times 100$

=$\frac{10}{52.5}\times 100=19.05$

and ,

Coefficient of variation in wage in firm B = $=\frac{{\sigma }_2}{\overline{X_2}}\times 100$

= $\frac{11}{47.5}\times 100=23.16$

Clearly, coefficient of variation in wages is greater for firm B than for firm A.

So , firm B shows more variability in wages.