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M11-28

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:45
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35% (medium)

Question Stats:

57% (00:48) correct 43% (00:35) wrong based on 60 sessions

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Is the standard deviation of set $$S$$ greater than the standard deviation of set $$T$$?

(1) The range of set $$S$$ is greater than the range of set $$T$$

(2) The mean of set $$S$$ is greater than the mean of set $$T$$

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16 Sep 2014, 00:45
Official Solution:

Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

(1) The range of set $$S$$ is greater than the range of set $$T$$. This implies that the biggest and smallest numbers in $$S$$ are more widespread than the biggest and smallest numbers in $$T$$. But what about the other numbers of these sets?

SD of {0, 10} is greater than SD of {0, 9}, but SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Not sufficient.

(2) The mean of set $$S$$ is greater than the mean of set $$T$$. Info about the mean is totally useless to get how widespread the given sets are. Not sufficient.

(1)+(2) Statement (2) gives absolutely no new info for (1), so even taken together they are still insufficient to answer the question.

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11 Jul 2016, 04:06
Hi

For this question I think St1 is sufficient as according Gmat Club math book, when we have to compere the standard deviation of two sets, always look for set with the largest range, because remote points have a very significant contribution to standard deviation.
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11 Jul 2016, 04:39
shanahit wrote:
Hi

For this question I think St1 is sufficient as according Gmat Club math book, when we have to compere the standard deviation of two sets, always look for set with the largest range, because remote points have a very significant contribution to standard deviation.

SD of {0, 10} is greater than SD of {0, 9}, but SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Not sufficient.
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11 Jul 2016, 04:58
Bunuel wrote:
shanahit wrote:
Hi

For this question I think St1 is sufficient as according Gmat Club math book, when we have to compere the standard deviation of two sets, always look for set with the largest range, because remote points have a very significant contribution to standard deviation.

SD of {0, 10} is greater than SD of {0, 9}, but SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Not sufficient.
D

SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is 3.31
SD of {0, 9} is 2.012
St1 is sufficient
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11 Jul 2016, 05:18
shanahit wrote:
Bunuel wrote:
shanahit wrote:
Hi

For this question I think St1 is sufficient as according Gmat Club math book, when we have to compere the standard deviation of two sets, always look for set with the largest range, because remote points have a very significant contribution to standard deviation.

SD of {0, 10} is greater than SD of {0, 9}, but SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Not sufficient.
D

SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is 3.31
SD of {0, 9} is 2.012
St1 is sufficient

No, that's not correct.

The (population) standard deviation of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is $$\sqrt{10} \approx 3.16$$: http://www.wolframalpha.com/input/?i=po ... ,+9,+10%7D
The (population) standard deviation of {0, 9} is 4.5: http://www.wolframalpha.com/input/?i=po ... %7B0,+9%7D
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18 Nov 2016, 02:23
HI ,

PLEASE HELP ME WITH THIS QUESTION. ALWAYS THOUGH AND THUS FAR HAVE READ THAT GREATER THE RANE LARGER THE SD. HENCE AS PER MY READING STMT 1 SHOULD BE ENOUGH.
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18 Nov 2016, 02:38
warpedhobbit wrote:
HI ,

PLEASE HELP ME WITH THIS QUESTION. ALWAYS THOUGH AND THUS FAR HAVE READ THAT GREATER THE RANE LARGER THE SD. HENCE AS PER MY READING STMT 1 SHOULD BE ENOUGH.

Please check the links below to brush up fundamentals on SD and statistics:

Hope it helps.
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19 Aug 2017, 16:08
Consider two examples:

S is {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6} and T is {-4, 4}. Meets restrictions of (1) and (2), and the answer to the prompt is no.
S is {-4, 6} and T is {-4, 4}. Meets restrictions of (1) and (2), and the answer to the prompt is yes.

Insufficient.
Re: M11-28   [#permalink] 19 Aug 2017, 16:08
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