Here xi = i, where i = 1, 2, …, n
Let x̄ be the mean and σ be the S.D.
x̄ = (1/n) Σxi = (1/n)(1 + 2 + 3 + … + n)
= (1/n) × [n(n+1)/2] = (n+1)/2
Variance (σ2) = (1/n) Σxi2 - (x̄)2
= (1/n)(12 + 22 + … + n2) - ((n+1)/2)2
= [n(n+1)(2n+1)]/(6n) - (n+1)2/4
= (n+1)(2n+1)/6 - (n+1)2/4
= [2(2n2 + 3n + 1) - 3(n2 + 2n + 1)]/12
= (n2 - 1)/12