Given N, a mean, a standard deviation, and the range, what does that tell us about the median? Obviously and trivially it must be within the range, but can we get tighter limits? To give context, I'm trying to find a median by repeated search. I may not rearrange the data and I get charged for each pass through it. So the tighter the limits on the initial estimate the better, and I can obtain range, mean and standard deviation from one pass.