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Topic: Re[2]: Quartiles
Replies: 0

 Bob Hayden Posts: 2,384 Registered: 12/6/04
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 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (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 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (work)