A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure is 40. Find the correct mean and S.D.

Given, Uncorrected mean is 40 and corrected SD is 5.1 and N = 100

To Find: Find the correct mean and SD

Explanation: Here,

Then,

The corrected sum of observation

So,

Now, Given Incorrect SD = 5.1

Corrected

Correct SD is 5

Hence, Correct mean is 39.90 and correct SD is 5