The mean of 30 observations was 15. Upon checking, it was found that two observations were wrongly taken as 2 and 5. If incorrect observations are replaced by the corrected values 7 and 11, then the corrected mean is?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15.36
The mean is the sum of the observations divided by their number. So the wrong mean gives the wrong sum; the wrong values are taken out of it, the correct ones put in, and the corrected sum is divided by 30 again.
The sum used for the wrong mean: \(30\times15=450\)
Taking out 2 and 5 and putting in 7 and 11: \(450-(2+5)+(7+11)=461\)
The corrected mean is this sum over 30 observations: \(\displaystyle\frac{461}{30}=15.36\ldots\)