The following results show the number of workers

Question:

The following results show the number of workers and the wages paid to them in two factories $F_{1}$ and $F_{2}$

Which factory has more variation in wages?

 

Solution:

Mean wages of both the factories are the same, i.e., Rs. 5300.

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 81 .

Now, $S D$ of factory $A=\sqrt{100}=10$

And, $S D$ of factory $B=\sqrt{81}=9$

Therefore,

The $\mathrm{CV}$ of factory $\mathrm{A}=\frac{10}{5300} \times 100=0.189$

The $C V$ of factory $B=\frac{9}{5300} \times 100=0.169$

Here, the CV of factory A is greater than the CV of factory B.

Hence, factory A has more variation.

 

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