The mean and standard deviation of 20 observations are found to be 10 and 2 . respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

Step-by-step solution

aligned & Mean ( x )=10 & x _ i 20 =10 & x _ i =10 20=200 aligned If 8 is replaced by 12, then x_i=200-8+12=204 Correct mean ( x )= x _ i 20 = 204 20 =10.2 Standard deviation =2 Variance =( S.D. )^2=2^2=4 x _ i ^2 20 - ( x _ i 20 )^2=4 x _ i ^2 20 -(10)^2=4 x _ i ^2 20 =104 x_i^2=2080 Now, replaced ' 8 ' observations by ' 12 ' Then, x _ i ^2=2080-8^2+12^2=2160 Variance of removing observations aligned & x_i^2 20 - ( x_i 20 )^2 & 2160 20 -(10.2)^2 & 108-104.04 & 3.96 aligned Correct standard deviation = 3.96