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I’m trying to compute the variance of how much pumpkins weigh across pumpkins from 125 farms. However, I only have, for each farm, three pieces of data: (1) the variance of weights for pumpkins from that farm (2) how many pumpkins the farm has (3) the total weight of the pumpkins from the farm.

How can I compute a “weighted variance” of how much a pumpkin weighs across farms? Can I just compute a weighted average of the individual variances?

kjetil b halvorsen
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John Hoffman
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    I hope you also have information about the weights in each farm--either total or average--for that is needed to obtain an answer. – whuber Sep 24 '14 at 20:07
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    Hmm, ok, lets assume that I also have the total weight in each farm. – John Hoffman Sep 24 '14 at 20:31
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    This sounds like the question at http://stats.stackexchange.com/questions/43159 on computing pooled variances but with $2$ groups replaced by $125$. Is that correct? If so, it may be worth observing that the solution there extends directly (and in the obvious manner) to your situation. – whuber Sep 24 '14 at 20:37

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