here are a bit of data from minitab ... that you might want to consider
MTB > rand 1000 c1-c25; <<< i generated 1000 samples that will be n=25 ...
SUBC> chis 4. <<< from a chisquare distribution with 4 degrees of freedom ...
MTB > rmean c1-c25, c26 <<< i put the MEAN for each row (sample mean) in c26
MTB > rmedian c1-c25, c27 <<< i put the MEDIAN for each row (sample median)
in c26
MTB > desc c26 c27
Descriptive Statistics: C26, C27
Variable N Mean Median TrMean StDev SE Mean
C26 1000 4.0380 4.0171 4.0260 0.5872 0.0186
C27 1000 3.4308 3.3670 3.4134 0.6636 0.0210
Variable Minimum Maximum Q1 Q3
C26 2.6021 5.7545 3.6410 4.3873
C27 1.7132 5.6370 2.9718 3.8435
a chisquare distribution with 4 df will exhibit considerable + skew ...
with mean being = df and, median then being less than mean ... it is about
3.4 here ...
if you want to estimate the population mean ... you can do that with the
sample mean ... if you want to estimate the population median, you can do
that with the sample median
and, just like building a CI for the population mean ... we can build a CI
for the population median ... one just has to make up their mind about what
they are trying to estimate
however, look at the sampling distributions of the mean and the median
note that both look approximately normal ... but, the STDEV in the above
describe data show that the sample MEAN has less error than the sample
median ... ie, the sample median is more likely to be a further distance
from the population median than the sample mean is likely to be away from
the population mean ..
you might want to consult an intermediate stat book for a procedure for
finding the CI for a median ... though in minitab, it is given as part of
the %decribe macro
MTB > dotp c26 c27;
SUBC> same.
Dotplot: C26, C27
Each dot represents up to 4 points
.
: : .
::...: :
::::::::::
: ::::::::::: .
::::::::::::::.:. .
::::::::::::::::::::.:
.. :::::::::::::::::::::::.:.. .
..::::::::::::::::::::::::::::::::::....
-+---------+---------+---------+---------+---------+-----C26
Each dot represents up to 4 points
. .
:: :
: ::.: :.:
. ::::::::::::
::.:::::::::::::..:
. .:::::::::::::::::::: .
.::::::::::::::::::::::::::::..
.......::::::::::::::::::::::::::::::::::...... .
-+---------+---------+---------+---------+---------+-----C27
1.60 2.40 3.20 4.00 4.80 5.60
MTB >
At 09:16 AM 1/31/01 -0800, James Ankeny wrote:
> Hello,
> I am currently taking a first course in statistics,
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