There are 50 numbers .Each number is subtracted from 53 and the mean so obtained is found to be -3.5.determine the mean of the given numbers

Question

This question is of book for diploma engineering named engineering mathematics.

Answer 1

What the problem tells you is that the sum of (53-xi) for i=1 to 50 divided by 50 = -3.5.

That equation becomes 50*53 - sum of xi for i = 1 to 50 = 50 * (-3.5),

then 2650 - sum(xi) for i =  1 to 50 = -175

Collecting terms gives sum xi for i=1 to 50 = 2825

The mean (average) of the numbers then is just 2825/50 = 56.5.