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 were omitted.

Question

Philoid · Accepted Answer

To Find: Find the correct mean and standard deviation.

Explanation: Here, n=100,

X =

So, Corrected

Corrected

Now, Standard variance = 3

Since, Variance =

Variance = 9

X =

9 =

Corrected

Correct mean =

Corrected Variance =

409.22-400

Corrected variance =9.22

Now, Corrected Standard Deviation =

Correct Deviation is 3.04

Hence, The correct Mean is 20 and Correct SD is 3.04