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