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?