1

Suppose that 2 persons collect samples of a random variable X. Each of them come up with : - the number of observations - the mean - the variance

How can we calculate the variance of all the observations ? Is there an exact calculus or an approximation.

Arnaud Mégret
  • 546
  • 4
  • 13
  • Does this Q&A http://stats.stackexchange.com/questions/163179/recover-true-statistics-for-a-union-of-subsamples-only-data-available-are-summ?noredirect=1&lq=1 help, especially the links provided in the comments? – mdewey Jan 19 '17 at 14:56

1 Answers1

0

Yes. We can compute exactly (and elegantly) the variance. The variance is the sum of - The average of the variance within each group - The variance of the means (weighted by the number of observations)

Notice that a similar result exists for mutual information

All the theory is there : http://www.burtonsys.com/climate/composite_standard_deviations.html

Arnaud Mégret
  • 546
  • 4
  • 13