How to get statistics of all samples through statistics of subsamples?

Question

I know the statistics of several subgroups.

For example,

Mean, variance, standard deviation, and number of group A
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

is 'number' a statistic? If so, what is it? – Dayne Mar 10 '21 at 07:57 — Dayne, Mar 10 '21 at 07:57
@Dayne 'number' is the count of elements in the group. – JHoon Mar 11 '21 at 00:26 — JHoon, Mar 11 '21 at 00:26

score 0 · Accepted Answer · answered Mar 10 '21 at 16:56

0

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.

answered Mar 10 '21 at 16:56

chrishmorris

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Can you give more explanation for sum(a^2 | a in A)? The expression (a^2 | a in A) is not well understood. – JHoon Mar 11 '21 at 00:28
The sum of the square of elements in A. – chrishmorris Mar 12 '21 at 11:32

How to get statistics of all samples through statistics of subsamples?

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