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Re[2]: Quartiles
Posted:
Mar 12, 1997 9:46 PM


 Forwarded message from Pat Ballew 
Alan Hutson wrote, in part " ii) Estimators of the percentiles are not uniquely defined, but some are more optimal than others in terms of bias and variability. For example, suppose we want to estimate the median. We could average the three middle observations or just use the intro to stat definition and use the middle observation as the estimator of the median. If the population is symmetric both estimators will be unbiased estimators of the population median, yet by using the three middle observations we would reduce the variablility of the estimator of the median substantially. Alan Hutson I'm not sure I understand the reason that the average of the three middle observations would be a "less" biased estimate of the median than the middle observation by itself. If we extend the number of "center" values averaged to higher levels (center 5 or 7 or 333) we would be moveing closer to the mean (and thus away from the median). Perhaps there is some probability idea at work that I don't see or understand. Could Alan or someone please explain. Pat Ballew Misawa, Japan 
Alan did not say "less biased" but less variable from sample to sample. If the population is symmetric, the mean and median are the same, so estimating the population median with the sample mean would be unbiased, so there is no bias to reduce. _   Robert W. Hayden   Department of Mathematics /  Plymouth State College MSC#29   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)
 End of forwarded message from Pat Ballew 

_   Robert W. Hayden   Department of Mathematics /  Plymouth State College MSC#29   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



