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POFinding mean with least number of iterations
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copied!<p>I have a list of measurements with the following properties:</p> <ol> <li>The measurements are expensive. Fewer measurements -> better</li> <li>They are all positive. In fact, there is a positive lower limit and I can't get any values below that. This lower limit is what I need to know with some confidence.</li> <li>They will distribute around one or more median values</li> <li>I know that there is another "better" median when I find an outlier which is smaller than <code>median - 2*variance</code> because the distance between the "best" median and the lower limit is always smaller than two times the width of the normal distribution</li> </ol> <p>Goal: Find the best median with the least amount of iterations with a confidence of, say, 90%.</p> <p>I'd prefer the smallest value but the smallest median is good enough.</p> <p>What I'm looking for is a piece of code where I feed the measurements and which tells me the median and how confident it is that this median is the one I seek.</p> <p>Background: I want to time Java methods. I could run the test for a couple of minutes to average outliers out but when looking at the data, it's pretty obvious for a human that the values quickly accumulate around the median value.</p> <p>Unless the JIT kicks in and the median suddenly jumps. Eventually, you will end up with a curve that is very steep left of the smallest median (i.e. the variance on the left side of the median is low) and a long, soft slope on the right side with a bump where the pre-JIT median was.</p> <p><a href="http://www.pdark.de/7ac2ce265a6a19ff53cb8591536ce8c2eae8ea74/performance.zip" rel="nofollow">Sample test data (13KB)</a></p> <p><code>testConnect-count.csv</code> is a histogram of the values, <code>testConnect-history.csv</code> is the sequence of measurements. The goal is find an algorithm which returns the smaller median around <code>115000</code> by reading the smallest number of values from <code>testConnect-history.csv</code></p>

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