The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on, it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.
It is given in the question that,
Total number of observations (n) = 100
Incorrect mean, (
) = 20
And, Incorrect standard deviation (
) = 3
Thus, incorrect sum of observations is 2000
Now, correct sum of observations = 2000 – 21 – 21 – 18
= 2000 – 60
= 1940
= 20
= 40900 – 441 – 441 – 324
= 40900 – 1206
= 39694
= 3.036
8