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Do you know statistics? by Tinton
Started on: 09-05-2006 10:19 PM
Replies: 10
Last post by: blakeinspace on 09-07-2006 10:51 AM
Tinton
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Report this Post09-05-2006 10:19 PM Click Here to See the Profile for TintonSend a Private Message to TintonDirect Link to This Post
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.
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Tinton
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Report this Post09-05-2006 11:31 PM Click Here to See the Profile for TintonSend a Private Message to TintonDirect Link to This Post
20 views and no replies, are you all stumped?
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Old Lar
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Report this Post09-05-2006 11:31 PM Click Here to See the Profile for Old LarSend a Private Message to Old LarDirect Link to This Post
What little I remember from statistics.

1.. 40
2.. 63
3.. 69
4.. 71
5.. 72
6.. 80
7.. 85
8.. 100
9.. 100
10.. 100


mean Average 78
median 76

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).]

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Tinton
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Report this Post09-05-2006 11:35 PM Click Here to See the Profile for TintonSend a Private Message to TintonDirect Link to This Post
Nice Lar! Thanks! If I didn't already have you as positive you'd be getting another!
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TK
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Report this Post09-05-2006 11:49 PM Click Here to See the Profile for TKSend a Private Message to TKDirect Link to This Post
I know that 51% of the people are in the majority.....
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Marvin McInnis
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Report this Post09-06-2006 01:03 AM Click Here to See the Profile for Marvin McInnisClick Here to visit Marvin McInnis's HomePageSend a Private Message to Marvin McInnisDirect Link to This Post
 
quote
Originally posted by Old Lar:

1.. 40
2.. 63
3.. 69
4.. 71
5.. 72
6.. 80
7.. 85
8.. 100
9.. 100
10.. 100


mean 78
median 76



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

Edit: I was wrong concerning the median. See below.

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

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jstricker
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Report this Post09-06-2006 08:31 AM Click Here to See the Profile for jstrickerClick Here to Email jstrickerSend a Private Message to jstrickerDirect Link to This Post
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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Marvin McInnis
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Report this Post09-06-2006 10:36 AM Click Here to See the Profile for Marvin McInnisClick Here to visit Marvin McInnis's HomePageSend a Private Message to Marvin McInnisDirect Link to This Post
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)/2th element; if N is even, the median is the N/2th 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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jstricker
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Report this Post09-06-2006 10:59 PM Click Here to See the Profile for jstrickerClick Here to Email jstrickerSend a Private Message to jstrickerDirect Link to This Post
Bingo.

This is the key.

"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)/2th element; if N is even, the median is the N/2th 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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Marvin McInnis
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Report this Post09-07-2006 12:21 AM Click Here to See the Profile for Marvin McInnisClick Here to visit Marvin McInnis's HomePageSend a Private Message to Marvin McInnisDirect Link to This Post
 
quote
Originally posted by jstricker:

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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blakeinspace
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Report this Post09-07-2006 10:51 AM Click Here to See the Profile for blakeinspaceClick Here to Email blakeinspaceSend a Private Message to blakeinspaceDirect Link to This Post
98% of all statistics are made up on the spot.
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