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I know the statistics of several subgroups.

For example,

  1. Mean, variance, standard deviation, and number of group A
  2. Mean, variance, standard deviation, and number of group B

Group C = Group A + Group B

With this information, can you find the mean, variance, standard deviation, and number of group C?

Assuming that the values of each group are unknown

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  • $\begingroup$ is 'number' a statistic? If so, what is it? $\endgroup$
    – Dayne
    Commented Mar 10, 2021 at 7:57
  • $\begingroup$ @Dayne 'number' is the count of elements in the group. $\endgroup$
    – JHoon
    Commented Mar 11, 2021 at 0:26

1 Answer 1

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Is C the disjoint union of A and B? If so, then

count(C) = count(A) + count(B) sum(C) = sum(A) + sum(B) sum(c^2 | c in C) = sum(a^2 | a in A) + sum(b^2 | b in B)

From these, you can work out mean, variance, and standard deviation.

Alternatively, are you wanting to estimate the statistics of a population C, based on samples of subpopulations A and B? That is more complicated, but searching for "Capture Re-capture" will give you a head start.

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  • $\begingroup$ Can you give more explanation for sum(a^2 | a in A)? The expression (a^2 | a in A) is not well understood. $\endgroup$
    – JHoon
    Commented Mar 11, 2021 at 0:28
  • $\begingroup$ The sum of the square of elements in A. $\endgroup$
    – chrishmorris
    Commented Mar 12, 2021 at 11:32

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