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, -10 on 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 Now, variance =( S.D. )2=8.25)2=8.25