The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases :
(i) If wrong item is omitted
(ii) if it is replaced by 12.
Given: Mean = 10
And, standard deviation = 2
We know that,
When wrong item is omitted,
Corrected mean
When it is replaced by 12,
Corrected mean
Now, for standard deviation,
Variance = (2)2 = 4
And we know that,
Now, omitting the wrong observation, we get,
Corrected Deviation
Now, replacing the observation
Corrected Deviation