Question

After settlement , the average weekly wage in a factory had increased from Rs. 8 to 12 and standard deviation had increased from Rs. 1 to 1.5 . The wages have become higher and more uniform , after settlement . Comment. ​

Answer 1

The statement that the wages have become higher after settlement is correct but the statement that the wages have become more uniform after settlement is not correct.

Step-by-step explanation:

We are given that after settlement, the average weekly wage in a factory had increased from Rs. 8 to 12 and standard deviation had increased from Rs. 1 to 1.5.

Here as we can clearly see that the average weekly wages in a factory have been increased from Rs 8 to Rs 12 which means that the statement that the wages have become higher is correct because there is an increment in the wages of the workers.

Now, to check whether the wages have become more uniform after settlement, we will use the Coefficient of Variation(C.V.) method.

Coefficient of Variation (C.V.)  =  $\frac{\text{Standard deviation}}{\text{Mean}}\times 100$

So, before settlement; the mean was = 8 and the standard deviation = 1.

The coefficient of variation before settlement =  $\frac{1}{8}\times 100$

                                                                             =  12.5%

Now, after settlement; the mean is = 12 and the standard deviation = 1.5.

The coefficient of variation after settlement =  $\frac{1.5}{12}\times 100$

                                                                         =  12.5%

As we can see that there is no change in the coefficient of variation after settlement, so we can conclude that the statement that the wages have become more uniform after settlement is not correct.