The variance of two running variances [duplicate]

Question

Having 2 sets, and only this data for each one, the running variance, the sum, the running mean and the count. How can I get the merged variance of the 2 sets?

EDIT:

The values of the sets are being updated each time with new ocurrences this ocurrences are not being stored.

The values of the sets are not equal.

I need to merge this 2 sets and get the new variance of this merged set.

EDIT 2:

I think that what I need is the pooled variance, am I correct?

In java would be something like this

Double variance = (((firstAggregate.count - 1) * firstAggregate.variance) + ((secondAggregate.count - 1) * secondAggregate.variance)) / ((otherAggregate.count + secondAggregate.count) - 2);

Answer 1

There's no need to merge two sets and compute the variance, it's a time consuming task you can compute the variance for each of them separately, then update the total variance. Updating variance could be done by using an update formula.

$T_1,_m = \sum_{i=1}^{m} x_i \\$

$S_1,_m = \sum_{i=1}^{m} (x_i - \frac{1}{m}*T_1,_m)^2 \\$

The equation discussed at a pairwise algorithm for computing sample variances paper.

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Update

Parallel algorithm