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M01-16

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M01-16 [#permalink]

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Official Solution:

\(Q\) is a set of 10 numbers. If the range of \(Q\) is zero, then what is the standard deviation of \(Q\)?

A. 0
B. 1
C. 3.33
D. 5
E. 10


In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, then the standard deviation is 0.

Notice that the standard deviation of a set is always more than or equal to zero: \(SD \geq 0\). SD is 0 if and only if a set contains all identical elements (or the set consists of only 1 element).


Answer: A
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Re: M01-16 [#permalink]

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New post 31 Oct 2014, 10:05
Dear Bunnuel,
You explained "In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, then the standard deviation is 0." but I suppose it is not always true.
For example, the range of the set consisting (-10, 1,2,....8,9,10) is still 0 but the set contains different elements.
Please correct me if I'm wrong.
Thank you!
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Re: M01-16 [#permalink]

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haihai89 wrote:
Dear Bunnuel,
You explained "In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, then the standard deviation is 0." but I suppose it is not always true.
For example, the range of the set consisting (-10, 1,2,....8,9,10) is still 0 but the set contains different elements.
Please correct me if I'm wrong.
Thank you!


You are wrong.

The range is the difference between the largest element and the smallest element of a set.

So, the range of (-10, 1,2,....8,9,10) is 10 - (-10) = 20, not 0.
_________________

New to the Math Forum?
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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: M01-16 [#permalink]

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New post 15 May 2017, 04:46
Dear Sir,

I have a doubt. What happens if my set is (1,3,6,7,7,7,8,9,9,11)
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Re: M01-16 [#permalink]

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New post 15 May 2017, 04:59
Manoraaju wrote:
Dear Sir,

I have a doubt. What happens if my set is (1,3,6,7,7,7,8,9,9,11)


Your doubt is not clear. The range is the difference between the largest element and the smallest element of a set.

So, the range of (1,3,6,7,7,7,8,9,9,11) is 11 - 1 = 10, not 0 as given in the stem.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
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Re: M01-16   [#permalink] 15 May 2017, 04:59
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