Hi,

(I hope this is not too basic)

I basically have a set of data from the same underlying distribution (which I would like to estimate), but I only have available the mean and N from partitions of the data. I can estimate the mean using a weighted average, and, I thought, the sample variance using weighted variance (e.g: https://stat.ethz.ch/pipermail/r-help/2008-July/168762.html)

However, I can't make much sense of the results. And I suspect I'm misunderstanding how/what weighted sample average should work.

**Edit:** From a set of (unobserved) data points all drawn from some distribution with some $\mu$ and $\sigma$, I can observe only the average and cardinality for partitions of the data. I.e. my observed values $X_i$ are each the average of some partition of size $N_i$, and thus have, $\mu_i=\mu$ and a $\sigma_i=\sigma/\sqrt{N_i}$.

**Question**: how can I estimate $\mu$ and $\sigma$ from the observed $X_i$s? Note that I can't observe the variance (or any other parameters) for the partitions.

The goal is to identify partitions that do not fit the expected distribution, i.e. identify partitions where $X_i$ is too many $\sigma_i$s from $\mu$.

doesappear too basic for this site, although like mikitov I'm not 100% sure I understand what you mean. Did you consider asking your question on stats.stackexchange.com – Thierry Zell May 6 '11 at 13:39