The mean of 40 observations was 34. Upon checking, it was found that two observations were wrongly copied as 4 and 7. If incorrect observations are replaced by the corrected values 11 and 13, then find the corrected mean.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 34.325
The mean is the sum divided by the number of observations, so the wrong sum is found from the given mean, corrected, and divided again by 40.
Sum as copied \(=40\times34=1360\)
Correct sum: remove the wrong values \(4+7=11\) and add the right ones \(11+13=24\): \(1360-11+24=1373\)
Corrected mean \(\displaystyle =\frac{1373}{40}=\) 34.325