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Set S has a mean of 10 and a standard deviation of 1.5. We are going

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Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?

A. {2, 10}
B. {10, 18}
C. {7, 13}
D. {9, 11}
E. {16, 16}

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[Reveal] Spoiler: OA

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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: Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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New post 06 Mar 2015, 07:37
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Bunuel wrote:
Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?

A. {2, 10}
B. {10, 18}
C. {7, 13}
D. {9, 11}
E. {16, 16}

Kudos for a correct solution.


The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 10,the values (9,11) are closer than others.
Hence Answer should be D

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Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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New post 07 Mar 2015, 10:52
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Hi,

To decrease the standard deviation, we should add values that are closer to the mean. The best bet would be two 10s. However, we don't have two 10s in the options. The next best values are 9, 11 , both within 1 point of the mean. Rest all far away and will increase the SD rather than decreasing it.

Thanks!

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Re: Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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Bunuel wrote:
Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?

A. {2, 10}
B. {10, 18}
C. {7, 13}
D. {9, 11}
E. {16, 16}

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

This is a very tricky problem. Starting list has mean = 10 and standard deviation of 1.5.

(A) {2, 10} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly decrease the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. WRONG

B. {10, 18} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly increase the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. BTW, (A) & (B) are essentially the same change — add the mean and add one number eight units from the mean. WRONG

C. {7, 13} — centered on 10, so this will not change the mean. Both of these are a distance of 3 units from the mean, and this is larger than the standard deviation, so it increases the size of the typical deviation from the mean. WRONG

D. {9, 11} — centered on 10, so this will not change the mean. Both of these are a distance of 1 units from the mean, and this is less than the standard deviation, so it decreases the size of the typical deviation from the mean. RIGHT

E. {16, 16} — these are two values far away from everything else, so this will wildly increase the standard deviation. WRONG

Answer = D.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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New post 07 Oct 2015, 01:39
Numbers closer to Mean, i.e 10 will decrease SD most

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Re: Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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Re: Set S has a mean of 10 and a standard deviation of 1.5. We are going [#permalink]

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New post 12 Oct 2017, 10:06
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D

Since 9 and 11 added to set S will not change the mean, and the distance from the mean to them is less than the standard deviation, the S.D will decrease.

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Re: Set S has a mean of 10 and a standard deviation of 1.5. We are going   [#permalink] 12 Oct 2017, 10:06
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