The variance of first n natural numbers
nn+12
n+1n+512
n+1n-512
n2-112
Explanation for correct option:
Step 1: Calculate the individual term
The first n natural number is 1,2,3,...,n
∴∑i=1ni=nn+12∑i=1ni2=nn+12n+16
Step 2: Calculate the Variance
Variance=∑i=1ni2n-∑i=1nin2
=nn+12n+16n-nn+12n2=n+12n+16-n+124=n+122n+1-3n+112=n+1n-112=n2-112
Hence, option D is correct.