Question

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

Answer 1

the mean of new is -3.5
so the old mean of given numbers is 49.5

Answer 2

Mean is nothing but Average, and the formula for it is,
Mean = Sum of Observation / No. of Observations,

To solve this question, 
Let the 50 numbers be , a1,a2,a3,a4,a5,........a50 ,
Here no. of Observations = 50,
And, Sum of all the 50 numbers = a1+a2+a3+.....+a50

Now according to the question,
( (53-a1)+(53-a2)+(53-a3)+............+(53-a50) ) / 50 = -3.5,
=> (53*50) - (a1+a2+a3+a4+......+a50) = 50*(-3.5)
=> (2650) + 185.5 = (a1+a2+a3+......+a50),
=> Sum of all the 50 numbers = 2835.5 ,

Now, we got all the required values to find mean of given numbers,
=> Mean of Given numbers = (a1+a2+a3+...+a50) / 50,
=> Mean of Given Numbers = 2835.5 / 50,
=> Mean of Given Numbers = 56.71,

Therefore the Answer to your question is 56.71 ,

Hope you understand, Have a Great Day ! Advance Merry Christmas !
Thanking you, Bunti 360 !