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


9