The arithmetic mean , the mode and the median of a group of 75 observations were calculate to be 27, 34 and 29 respectively. It was later discovered that one observation was wrongly read as 43 instead of the correct value 53. Examine to what extent the calculate values of the averages will be affected by the error.

Explanation

Given : N `=75,overline(X)=27`
we know , `overline(X)= (sumX)/(N) or sumX= Noverline(X)`
`:. sumX=75xx27=2,025`
Corrected `overline(X)=2,025-43+53=2,035`
Corrected `overline(X)=(2,035)/(75)=27.13`
Thus , the value of mean is affected ,. But the values of median and mode will be affected by this error because these are positional averages and the median value is 29 which is far away from the values 43 and 53 . Similarly , the value of mode would not be affected by the error since the modal value 34 is far away from the values 43 and 53.