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# Which of the following sets has the smallest standard deviation?

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Math Expert
Joined: 02 Sep 2009
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Which of the following sets has the smallest standard deviation?  [#permalink]

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11 Jan 2017, 03:48
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Difficulty:

25% (medium)

Question Stats:

79% (01:02) correct 21% (00:41) wrong based on 114 sessions

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Which of the following sets has the smallest standard deviation?

A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 4, 5, 6, 10}

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Which of the following sets has the smallest standard deviation?  [#permalink]

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11 Jan 2017, 12:05
Bunuel wrote:
Which of the following sets has the smallest standard deviation?

A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 4, 5, 6, 10}

First, We can see that all the choices have median as 5. Since we know that standard deviation is a measure of dispersion(or separation) of the elements from median, choose the set that has lowest range.
Option B and D have equal range -> 4.
To Choose between B and D, again if we compare each element from median, distance from 5 to first element 3 and last element 7 is same for both.
But in B separation from median is less than that of D for the middle elements. In B it is 1 and in D it is 2.

IMO B.
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Re: Which of the following sets has the smallest standard deviation?  [#permalink]

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11 Jan 2017, 12:15
Standard deviation depends on deviation.
A. {2,2,5,8,8} => {-3,-3,0,3,3}
B. {3,4,5,6,7} => {-2-1,0,1,2}
C. {1,3,5,7,9} => {-4,-2,0,2,4}
D. {3,3,5,7,7} => {-2,-2,0,2,2}
E. {0,4,5,6,10} => {-5,-1,0,1,5}

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Re: Which of the following sets has the smallest standard deviation?  [#permalink]

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28 Jan 2018, 09:04
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Re: Which of the following sets has the smallest standard deviation?   [#permalink] 28 Jan 2018, 09:04
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