If mean of squares of deviations of a set of n observation about -2 and 2 are 18 and 10 respect then standard deviation of this set of observations is

The variance is the mean of squared deviations about the mean. Let the mean be m and the variance be v. We know the sum of squares of deviations equals n(v + a^2) for any value a. So 18 = v + (-2 - m)^2 and 10 = v + (2 - m)^2. Subtracting the second from the first gives 8 = (-2 - m)^2 - (2 - m)^2 = 8m, so m = 1. Substituting m = 1 into 10 = v + 1 yields v = 9. The standard deviation is the square root of the variance, which is 3.

• Thanks
• Wrong explanation