I'm doing homework right now for Statistics class, anyone want to help? This one problem is really messing me up:

For each of the following properties, try to construct a data set of ten hypothetical exam scores that satisfies the property. Assume that the exam scores are integers between 0 and 100, inclusive. You may use a calculator.

e. the mean does not equal the median and none of the scores are between the mean and the median.

If the mean = average and the median means "middle" number. Of course median is 50% above and 50% below of some number. With this example no score is 78 or 76 and no score is 77, the value between the median and mean.

I was playing with Excel to generate this and there were several combinations that fit this.

[This message has been edited by Old Lar (edited 09-05-2006).]

Actually, that is one correct definition of a median as long as the dataset is an even number. How do you get the middle number of an even numbered dataset? You find the mean of the two middle values.

John Stricker

quote

Originally posted by Marvin McInnis:

Mean = 78 ... yes Median = 76 ... NO WAY! 76 isn't even present in the data set.

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08:31 AM

Marvin McInnis Member

Posts: 11597 From: ~ Kansas City, USA Registered: Apr 2002

I was always taught ... and the professional (i.e. PhD) statisticians I have worked with have always required ... that the median must be present in the data set: if N is odd, the median is the (N + 1)/2^{th} element; if N is even, the median is the N/2^{th} element.

Taking the mean of the two middle values does make sense for a sparse (small) data set ... but statistical analysis is not very meaningful for such data sets anyway, unless the range of values is very small.

As the size of the data set grows, the usefulness of taking the mean of the two middle values when N is even diminishes substantially.

[This message has been edited by Marvin McInnis (edited 09-06-2006).]

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10:36 AM

jstricker Member

Posts: 12956 From: Russell, KS USA Registered: Apr 2002

"but statistical analysis is not very meaningful for such data sets anyway, unless the range of values is very small"

Small datasets are nearly useless for meaningful statistical PREDICTION, but not all that useless for analysis. Just don't expect the statistics to be able to forecast much.

Now, my son, say two "Hail Gottfried Achenwall"'s and go in peace to sin no more.

John Stricker

quote

Originally posted by Marvin McInnis:

I stand corrected! My apologies to all.

I was always taught ... and the professional (i.e. PhD) statisticians I have worked with have always required ... that the median must be present in the data set: if N is odd, the median is the (N + 1)/2^{th} element; if N is even, the median is the N/2^{th} element.

Taking the mean of the two middle values does make sense for a sparse (small) data set ... but statistical analysis is not very meaningful for such data sets anyway, unless the range of values is very small.

As the size of the data set grows, the usefulness of taking the mean of the two middle values when N is even diminishes substantially.

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10:59 PM

Sep 7th, 2006

Marvin McInnis Member

Posts: 11597 From: ~ Kansas City, USA Registered: Apr 2002

Small datasets are nearly useless for meaningful statistical PREDICTION, but not all that useless for analysis.

...

Now, my son, say two "Hail Gottfried Achenwall"'s and go in peace to sin no more.

Mea culpa ... again! Bless me, father, for I have committed blasphemy against the Gods of variance.

"Small datasets are ... not all that useless for analysis" ... as long as you don't expect your results to actually mean anything. In general, intuition (or prejudice) is usually every bit as useful as statistical analysis for datasets where N < 100 or so.

This is all probably more than Tinton ever wanted to know, so I'll shut up now.

[This message has been edited by Marvin McInnis (edited 09-07-2006).]

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12:21 AM

blakeinspace Member

Posts: 5922 From: Fort Worth, Texas Registered: Dec 2001