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

Options

A. 46.5
B. 49.5
C. 53.5
D. 56.5

Answer

D

Explanation

`"Mean" = ("sum of all observations")/("total numbers of observations")`
`rArr -3.5= ((53-x_(1))+(53-x_(2))+(53-x_(3))+.....+(53-x_(50)))/(50)`
`rArr -3.5= ((53 xx50)-(x_(1)+x_(2)+x_(3)+.....+x_(50)))/(50)`
`rArr -3.5= (53 xx50-50bar(x))/(50)`
`rArr -3.5= 53-bar(x) rArr bar(x)=53+3.5=56.5`
Hence, (d) is the correct answer.