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Math Expert V
Joined: 02 Sep 2009
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Is the standard deviation of the scores of Class A’s students greater  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 84% (00:52) correct 16% (00:39) wrong based on 28 sessions

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Is the standard deviation of the scores of Class A’s students greater than the standard deviation of the scores of Class B’s students?

(1) The average (arithmetic mean) score of Class A’s students is greater than the average score of Class B’s students.
(2) The median score of Class A’s students is greater than the median score of Class B’s students.

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examPAL Representative P
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Re: Is the standard deviation of the scores of Class A’s students greater  [#permalink]

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The answer is E.

This question is resolved using the logic of standard deviation - SD is a measure of how spread out an average is. To find it, we need info about the variance of the values being checked, or the values themselves (the scores of students in each class). Without that information, finding standard deviation is impossible.
(Class A could have just 1 student with a higher score than the average in class B - meaning the SD is 0. Or it could have 2 student, one with a score 30 points higher and the other with a score 20 points lower - still a higher average and median, but a huge SD. We have no idea...)
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Re: Is the standard deviation of the scores of Class A’s students greater  [#permalink]

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Bunuel wrote:
Is the standard deviation of the scores of Class A’s students greater than the standard deviation of the scores of Class B’s students?

(1) The average (arithmetic mean) score of Class A’s students is greater than the average score of Class B’s students.
(2) The median score of Class A’s students is greater than the median score of Class B’s students.

Question: Is $$SD_A > SD_B$$?

CONCEPT: Standard deviation depends on the following two measures
1) The number of terms in the set
2) Separation between the terms when terms arranged in increasing order

Standard Deviation does NOT depend on
1) How big/small the terms are

Statement 1: The average (arithmetic mean) score of Class A’s students is greater than the average score of Class B’s students.
Greater Average of one set than the other set doesn't predict which set will have larger/smaller standard deviation hence
NOT SUFFICIENT

Statement 2: The median score of Class A’s students is greater than the median score of Class B’s students
Greater Median of one set than the other set doesn't predict which set will have larger/smaller standard deviation hence
NOT SUFFICIENT

Combining the two statements

Case 1:
Set A = {10, 11, 12, 13, 14}
Set B = {0, 1, 2, 3, 4}

Set A has higher mean and median than that of set B but the standard deviation of both sets are same

Case 2:
Set A = {10, 11, 12, 13, 14}
Set B = {0, 1, 2, 3, 5}

Set A has higher mean and median than that of set B but the standard deviation of Set A is smaller than Standard deviation of set B

Case 3:
Set A = {10, 11, 12, 13, 15}
Set B = {0, 1, 2, 3, 4}

Set A has higher mean and median than that of set B and the standard deviation of Set A is bigger than Standard deviation of set B

NOT SUFFICIENT

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