The mean of 50 observations was 46. Upon checking, it was found that two observations were wrongly copied as 5 and 8. If incorrect observations are replaced by the corrected values 12 and 14, then find the corrected mean.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 46.26
The mean is the sum of the observations divided by their number, so the wrong sum is corrected first: the two wrong values are taken out and the right ones put in. The number of observations stays 50.
Sum found earlier: \(50\times46=2300\)
Corrected sum: \(2300-(5+8)+(12+14)=2313\)
Corrected mean: \(\displaystyle\frac{2313}{50}=\) 46.26