Variance for 649

[Bertil]

After a set of six numbers have been drawn in a 649 game one can calculate the variance within the set. E.g for the set 1-2-3-4-5-6 it is 3.5
and for the set 1-2-3-47-48-49 it is 635.6 based on the variance formula with (N-1) as denominator rather than (N).

What would the mean variance be for all 14 million possible combinations?
There seems to be no general formula for predicting this for any n/N game.

Does anybody here have a cumulative mean variance for any 6/49 game and
if so, on how many draws was it based? I expect the value to be in the range
144-225.

Bertil

 

[Bertil]

I've just discovered a formula for the sample variance of any lotto n/N.
It seems to be N(N+1)/12. It is independent of n and can be verified
for 3/7 and 5/7, which both have a sample variance of 14/3 as does 2/7,
but the population variance would seem to depend on the factor (n-1)/n.

Bertil