Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is

The first 10 positive integers are 1,2,3,4,5,6,7,8,9 and 10.On multiplying each number by -1, we get-1, -2, -3, 4, -5, -6, -7, -8, -9, -10On adding 1 to each number, we get0, -1, -2, -3, -4, -5, -6, -7, -8, -9∴ Σxi    =−9×102=−45 and     Σxi2=02+(−1)2+(−2)2+…+(−9)2=9×10×196=285∴  S.D.     =28510−−45102=28510−2025100    =2850−2025100=8.25