Question

The following results show the number of workers and the wages paid to them in two factories A and B.

$\begin{array}{ccc}\text{Factory}& \text{A}& \text{B}\\ \text{Number of workers}& 4000& 5000\\ \text{Mean wages}& Rs3500& Rs3500\\ \text{Variance of distribution of wages}& 64& 81\end{array}$

Which factory has more variation in wages?

Answer 1

We have:

Variance of distribution of wages in factory A, ${\sigma }_1^2=64$

Variance of distribution of wages in factory B, ${\sigma }_2^2=81$

$\therefore$ (${\sigma }_1^2=64)$ and ${\sigma }_2^2=81$) $\Rightarrow$ (${\sigma }_1=8$ and ${\sigma }_2=9$).

Thus, SD of distribution of wages in factory A = 8.

And, SD of distribution of wages in factory B = 9.

Since the monthly mean wages in two factories are the same and ${\sigma }_1<{\sigma }_2$, hence, the factory B has more variation in wages.