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# Mrs. Hopkins has two math classes, each with the same number

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CIO
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Mrs. Hopkins has two math classes, each with the same number [#permalink]

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23 Jul 2004, 12:51
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Mrs. Hopkins has two math classes, each with the same number of students. What was the standard deviation of all her math students' scores on an identical test she gave both classes?

1) The standard deviation of the test scores in her first math class was 2 points.

2) The standard deviation of the test scores in her second math class was 2 points.
Director
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23 Jul 2004, 16:34
E
Means of the 2 samples can be different
Manager
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23 Jul 2004, 19:19
guys,
I need help with my stats. Its been a long time sinse I studied SD, mean, mode etc .can u guys point me to material that I could go through (preferably on the internet) . appreciate all the help in this regard

regards
Senior Manager
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23 Jul 2004, 23:47
I think it is E.

The only inference from the stem is that the total mean of the two classes is the average of the two means. Unless we have some kind of relationship about the marks, it is tough to determine individual means from either (1) or (2) or combined and thus the total deviation.

SD = sqrt(sum of squares of the mean deviations/total number of samples)

What we need to find out is the mean of all the students of both the classes and then compute the SD. By the very nature of the above formula(sqrt) and the statistics(two same groups may have different means but their mean deviations sum might be the same), we cannot say that SD = SD1+SD2 or anything of that kind.

ian7777 wrote:
Mrs. Hopkins has two math classes, each with the same number of students. What was the standard deviation of all her math students' scores on an identical test she gave both classes?

1) The standard deviation of the test scores in her first math class was 2 points.

2) The standard deviation of the test scores in her second math class was 2 points.

_________________

Awaiting response,

Thnx & Rgds,
Chandra

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24 Jul 2004, 00:13
Yup, you're all right! It is E. And the various explanations are all right.

For this question, you need to know that standard deviation alone means nothing without the average it's describing. If the test scores' SD was 2 for both classes, we don't know if they each averaged 85, or if one class averaged 80 while the other averaged 90. Without information about the actual test grades of the various students, we can't know what the standard deviation is.

Bottom line, you can't do anything with SD except describe the average. You certainly can't combine different ones in any meaningful way.
24 Jul 2004, 00:13
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