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Suppose there are two populations, optimists and pessimists. Optimists are more optimistic about the future economy and pessimists are more pessimistic. There are equal number of optimists and pessimists, I draw their forecasts from them and consider the median forecasts. Suppose there are news and their forecasts (the distributions of forecasts) change. Under what conditions that new forecasts will be more volatile from old forecasts (i.e. the variance of the median is larger)?

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What are the hypotheses? This does not make sense as stated -- voting to close. –  Igor Rivin Aug 9 '11 at 16:57
The question has nothing to do with order statistics from what I can tell. Voting to close as well. –  Steve Huntsman Aug 9 '11 at 17:17
Suppose there are two populations with distribution F and G. The draws are iid. We take n samples from both populations and pick a median. We calculate the distribution of the median and its variance. What kind of shifts on F and G will make the variance of the median larger? –  user16133 Aug 9 '11 at 18:45
stats.stackexchange.com may be better for this question –  David Roberts Aug 9 '11 at 21:59
...if it could be cleaned up to make sense (judging by others' comments) –  David Roberts Aug 9 '11 at 23:13
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