Consider the numbers 1 ,2,3, 4, 5, 6,7 ,8, 9 and 10. If 1 is added to each number, the variance of the numbers so obtained is

Given numbers are 1,2,3,4,5,6,7,8,9 and 10 . If 1 is added to each number, then observations will be 2, 3, 4, 5, 6,7 ,8, 9, 10 and 11.∴Σxi=2+3+4+…+11         =102[2×2+9×1]=5[4+9]=65 and Σxi2=22+32+42+52+…+112=12+22+32+…+112−12=11×12×236−1=505∴ V=s2=Σxi2n−Σxin2=50510−65102=50.5−(6.5)2=50.5−42.25=8.25