For a data consisting of 15 observations x_i , i=1,2,3, , 15 the following results are obtained : _ i=1 ¹⁵ x_i=170 ; _ i=1 ¹⁵ x_i^2=2830 . If one of the observation namely 20 was found wrong and was replaced by its correct value 30 , then the corrected variance is

Step-by-step solution

Given, x^2=2830 and x=170 Increase in x=10 and increase in x^2=(30)^2-(20)^2 aligned & =900-400=500 & x^ =170+10=180 & and x^ 2 =2830+500=3330 & We know that, variance = x^2 n - ( x n )^2 & = 3330 15 - ( 180 15 )^2 [here, n=15 ] & =222-144=78 aligned