I will try to explain with a mathematical example:-
Suppose, you have sample data with 4 outcomes.
Let their absolute deviation from mean are a,b,c,d.
We take sd ((a^2+b^2+c^2+d^2)/4)^0.5 ... (A)
You are thinking why not ((a^2+b^2+c^2+d^2)/4^2)^0.5 i.e. ((a^2+b^2+c^2+d^2)^0.5)/4 ... (B)
Let a=b=c=d. Now, ideally sd should be around same value as any deviance as all deviance are same.
Now, if you solve (A) & (B),
You'll get 'a' from (A) & 'a/2' from (B)
Hence, there is underestimation of sd from (B).
The sample size increases, so the underestimation from (B)
Last edited: Jul 16, 2017