I guess the next step might be finding the probability of n-1 out of n observations all being above (below) the median and then try to figure out how many observations you would need to have a 95% confidence in the median being between the second highest and second lowest observation.
I guess if you did this iteratively you could find an algorithm along the lines of: "With m independent observations the median is with 95% confidence between the k highest and k lowest observation."
Yeah, that would be pretty cool. I'm not sure, but perhaps if you assumed that the population distribution was symmetric, then the removal of the k highest and k lowest would have symmetric effects on the probabilities of being above/below the median for the remaining data, allowing them to stay 50-50. I'd have to work through the math though.
I guess the next step might be finding the probability of n-1 out of n observations all being above (below) the median and then try to figure out how many observations you would need to have a 95% confidence in the median being between the second highest and second lowest observation.
I guess if you did this iteratively you could find an algorithm along the lines of: "With m independent observations the median is with 95% confidence between the k highest and k lowest observation."
Yeah, that would be pretty cool. I'm not sure, but perhaps if you assumed that the population distribution was symmetric, then the removal of the k highest and k lowest would have symmetric effects on the probabilities of being above/below the median for the remaining data, allowing them to stay 50-50. I'd have to work through the math though.