The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?

Question

Philoid · Accepted Answer

To Find: Find the correct mean and standard deviation.

Explanation: Here, n=100,

X =

Now,

Corrected

3990

So, The mean of correct score =

Mean = 39.9

Now, Standard variance = 5.1

Since, Variance =

Variance = 26.01

X =

26.01 =

Corrected -50+40

Corrected

Corrected Variance =

1625.91-1592.01

Corrected variance =34 (Approx)

Now, Corrected Standard Deviation =

Correct Deviation is 5.83

Hence, The correct Mean is 39.9 and Correct SD is 5.83