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M11-28

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M11-28 [#permalink]

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New post 16 Sep 2014, 00:45
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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 \(T\)
[Reveal] Spoiler: OA

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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.


Answer: E
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New post 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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New post 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.


Please check the examples below:
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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Re: M11-28 [#permalink]

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New post 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.


Please check the examples below:
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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Re: M11-28 [#permalink]

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New post 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.


Please check the examples below:
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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M11-28 [#permalink]

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New post 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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New post 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.


No, your reasoning is wrong.

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


Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M11-28 [#permalink]

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New post 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.

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