Question

the mean of 100 observations is 50 if one of the observation which was 50 is replaced by 150, then find the resulting mean

Answer 1

let the 100 numbers be
x1,x2,x3,x4.........x89,x99,50

(x1+x2+x3+.....x99)+50/100 = 50

(x1+x2+x3+.....x99) = 5000-50 = 4950

Now the mean of
x1,x2,x3......x99,150

= (x1+x2+x3....x99)+150/100
= (4950+150)/100
= 5100/100
= 51

hence the mean is 51.