1. The monthly wages paid to the workers of a factory had a mean of Rs. 2,400 with the standard deviation of Rs. 250. What will be the new mean and standard deviation if the wages of all workers are increased by
  1. Rs. 300
  2. 10%

Dear Student

If wages of all workers are increased by 300 then the mean will also rise by 300 . So new mean = 2400+300=2700
This follows from the property of arithmetic mean . For the second case new mean = 2400+2400(10/100)=2400+240=2640

Now let us come to standard deviation . ​If you add the same number to every number on the list, or if you subtract the same number from every number on a list, or if you subtract each number on the list from the same number, all of the new lists produced would have exactly the same standard deviation as the original.  Addition and subtraction slides values up and down the number line, but does not change any of the spacing between the numbers. Standard deviation is nothing but spacing . So sd will remain the same in case 1 where 300 is added to each number .

But in the second case all the wages are multipled by 1+10/100=110/100 =11/10 . So sd will get multipled by 11/10 . Because multiplying or dividing changes the spacing . So new sd=250(11/10)=275 

Regards .


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