The mean and standard deviation of 100 observations are 40 and 5.1 , respectively, By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are and respectively, then 10( + ) is equal to

Step-by-step solution

aligned & Actual means = = 100(40)-50+40 100 & =40- 1 10 =39.9 aligned Incorrect variance aligned & (5.1)^2= x _ i ^2 100 -( x )^2 & x _ i ^2=100 (40^2 )+100(5.1)^2 & x _ i ^2=16 10^4+(5.1)^2 100=162601 & ^2= x _ i ^2-50^2+40^2 100 -( )^2 & ^2=1617.01-(39.9)^2=25 & =5 & 10( + )=10(39.9+5) & =10 44.9=449 aligned