Given n = the number of observations = 100, Mean = 40
Mean = sum of observations/total number of observations
40 = sum of the observations/ 100
Sum of the observations = 40 x 100
Thus, the incorrect sum of the observations = 40 x 100 = 4000.
Now,
The correct sum of the observations = Incorrect sum of the observations – Incorrect observation + Correct observation
The correct sum of the observations = 4000 – 83 + 53
The correct sum of the observations = 4000 – 30 = 3970
Correct mean = correct sum of the observations/ number of observations
= 3970/100
= 39.7
