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# Which set has the smallest standard deviation ?

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Which set has the smallest standard deviation ?  [#permalink]

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16 Dec 2018, 02:24
2
00:00

Difficulty:

45% (medium)

Question Stats:

48% (00:57) correct 52% (01:25) wrong based on 45 sessions

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Which of the following set has the smallest standard deviation ?

A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}

Kudos for right answer and detailed explanation

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Manager
Joined: 08 Sep 2008
Posts: 134
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: Which set has the smallest standard deviation ?  [#permalink]

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16 Dec 2018, 05:31
SD for any set is smallest if the numbers of sets are closely distributed.
If all the numbers of a given set is same SD is minimum i.e. ZERO.
Option
A: 2,2,3,5,7 Mean approx.~ 4
Distribution from mean: -2,-2,-2,1,3
B: 2,2,2,2,79 mean approx.: 17
Distribution from mean: -15,-15,-15,-15,+62
C: 2,2,3,4,7 mean Approx. 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.4
D: 2,2,3,4,6.9 mean approx: 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.3
E: 2,2,3,5,8: mean approx: 4
Distribution from mean: -2,-2,-1, +1,+4

Closely distributed: Option D.

Note we don’t need to calculate as above. Just a glance will give an idea about SD for option D is smallest.
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Vishal

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: Which set has the smallest standard deviation ?  [#permalink]

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16 Dec 2018, 07:04
Hi vishalkazone

Thank you. But could you show us another simpler approach based on comparison ?
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Re: Which set has the smallest standard deviation ?  [#permalink]

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20 Dec 2018, 20:07
vishalkazone wrote:
SD for any set is smallest if the numbers of sets are closely distributed.
If all the numbers of a given set is same SD is minimum i.e. ZERO.
Option
A: 2,2,3,5,7 Mean approx.~ 4
Distribution from mean: -2,-2,-2,1,3
B: 2,2,2,2,79 mean approx.: 17
Distribution from mean: -15,-15,-15,-15,+62
C: 2,2,3,4,7 mean Approx. 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.4
D: 2,2,3,4,6.9 mean approx: 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.3
E: 2,2,3,5,8: mean approx: 4
Distribution from mean: -2,-2,-1, +1,+4

Closely distributed: Option D.

Note we don’t need to calculate as above. Just a glance will give an idea about SD for option D is smallest.

Hello!

Why is the mean of D is close to 3.6?

2+2+3+4+6+9 = 26/6 = 4.3..
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Joined: 10 Jan 2014
Posts: 6
GPA: 3.6
Re: Which set has the smallest standard deviation ?  [#permalink]

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20 Dec 2018, 21:56
jfranciscocuencag wrote:
vishalkazone wrote:
SD for any set is smallest if the numbers of sets are closely distributed.
If all the numbers of a given set is same SD is minimum i.e. ZERO.
Option
A: 2,2,3,5,7 Mean approx.~ 4
Distribution from mean: -2,-2,-2,1,3
B: 2,2,2,2,79 mean approx.: 17
Distribution from mean: -15,-15,-15,-15,+62
C: 2,2,3,4,7 mean Approx. 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.4
D: 2,2,3,4,6.9 mean approx: 3.6
Distribution from mean: -1.6,-1.6,-0.6, +0.4,+3.3
E: 2,2,3,5,8: mean approx: 4
Distribution from mean: -2,-2,-1, +1,+4

Closely distributed: Option D.

Note we don’t need to calculate as above. Just a glance will give an idea about SD for option D is smallest.

Hello!

Why is the mean of D is close to 3.6?

2+2+3+4+6+9 = 26/6 = 4.3..

It is 6.9 I believe.
Re: Which set has the smallest standard deviation ?   [#permalink] 20 Dec 2018, 21:56
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