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Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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Difficulty:   25% (medium)

Question Stats: 76% (00:36) correct 24% (00:33) wrong based on 138 sessions

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Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}

A={1, 3, 5, 7, 9}

B={2, 4, 6, 8, 10}

C={1, -1, -3, -5, -7}

A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the sets

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Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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Official Solution:

Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}

A={1, 3, 5, 7, 9}

B={2, 4, 6, 8, 10}

C={1, -1, -3, -5, -7}

A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the sets

If we add or subtract a constant to each term in a set the standard deviation will not change.

Since each set can be obtained by adding some constant to each term of set X (20 for set A, 21 for set B and 12 for set C), the standard deviations of all sets are the same.

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Current Student S
Joined: 18 Aug 2014
Posts: 324

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Bunuel wrote:
Official Solution:

Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}

A={1, 3, 5, 7, 9}

B={2, 4, 6, 8, 10}

C={1, -1, -3, -5, -7}

A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the sets

If we add or subtract a constant to each term in a set the standard deviation will not change.

Since each set can be obtained by adding some constant to each term of set X (20 for set A, 21 for set B and 12 for set C), the standard deviations of all sets are the same.

Can someone please explain (Bunuel if you're listening I'd appreciate the clarification) what exactly the logistics behind "adding some constant to each term" means? I presume like this, if Set x is [1, 2, 3, 4, 5] and adding 20 to it you get [21, 22, 23, 24, 25]. but I'm not sure how this relates either to the standard deviation or to why Bunuel chose different numbers for each set "20 for set A, 21 for set B and 12 for set C"
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Math Expert V
Joined: 02 Aug 2009
Posts: 7742

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redfield wrote:
Bunuel wrote:
Official Solution:

Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}

A={1, 3, 5, 7, 9}

B={2, 4, 6, 8, 10}

C={1, -1, -3, -5, -7}

A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the sets

If we add or subtract a constant to each term in a set the standard deviation will not change.

Since each set can be obtained by adding some constant to each term of set X (20 for set A, 21 for set B and 12 for set C), the standard deviations of all sets are the same.

Can someone please explain (Bunuel if you're listening I'd appreciate the clarification) what exactly the logistics behind "adding some constant to each term" means? I presume like this, if Set x is [1, 2, 3, 4, 5] and adding 20 to it you get [21, 22, 23, 24, 25]. but I'm not sure how this relates either to the standard deviation or to why Bunuel chose different numbers for each set "20 for set A, 21 for set B and 12 for set C"
...

the addition is being done to the SET in Question stem - set X={-19, -17, -15, -13, -11}
1) add 20 to each item of X {-19+20, -17+20, -15+20, -13+20, -11+20}
{1,3,5,7,9} SAME as A={1, 3, 5, 7, 9}

2) add 21 to each item of X {-19+21, -17+21, -15+21, -13+21, -11+21}
{2, 4, 6, 8, 10} SAME as B={2, 4, 6, 8, 10}

1) add 12 to each item of X {-19+12, -17+12, -15+12, -13+12, -11+12}
{1,-1,-3,-5,-7} SAME asC={1, -1, -3, -5, -7}
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Current Student B
Joined: 31 Oct 2014
Posts: 5
Location: India
GMAT 1: 750 Q49 V42 GPA: 3.62

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I think this is a poor-quality question and I don't agree with the explanation. There is an error in Set C. The explanation says -19+12=-1? How is that possible?
Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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saumyasharma wrote:
I think this is a poor-quality question and I don't agree with the explanation. There is an error in Set C. The explanation says -19+12=-1? How is that possible?

The question is fine.

X = {-19, -17, -15, -13, -11}

+12

C = {-7, -5, -3, -1, 1} (it's the same set as {1, -1, -3, -5, -7} but in different order).
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Manager  S
Joined: 25 Mar 2013
Posts: 236
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

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Empowergmat Rich, Egmat cab you please explain the concept behind this question. How can I solve similar type of questions?
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Manager  S
Joined: 21 Jul 2017
Posts: 190
Location: India
GMAT 1: 660 Q47 V34 GPA: 4
WE: Project Management (Education)

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Bunuel wrote:
Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}

A={1, 3, 5, 7, 9}

B={2, 4, 6, 8, 10}

C={1, -1, -3, -5, -7}

A. Set A only
B. Set B only
C. Set C only
D. Sets A, B and C
E. None of the sets

Dear Bunuel,

Two sets dispersed equally along their mean have equal SD. Is this logic fine to solve this question? M05-07   [#permalink] 26 Oct 2018, 12:52
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