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# Is the standard deviation of set Q equal to 0?

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Senior Manager
Joined: 21 Oct 2013
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Is the standard deviation of set Q equal to 0?  [#permalink]

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02 Aug 2014, 04:49
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Difficulty:

35% (medium)

Question Stats:

62% (00:49) correct 38% (00:55) wrong based on 203 sessions

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Is the standard deviation of set Q equal to 0?

(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q.
(2) The median of set Q is equal to the greatest number in Q.
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Joined: 17 Nov 2013
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Concentration: Strategy, Healthcare
GMAT 1: 710 Q49 V38
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Re: Is the standard deviation of set Q equal to 0?  [#permalink]

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02 Aug 2014, 05:06
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Straight A.

Standard deviation is 0 if and only if all the elements are the same. Whether 1 element or 10 elements.

In that case, the mean will also be the same as the element in the set. That renders the largest element equal to the mean. Hence, A is Sufficient.

In B, the median can be equal to largest value and still have different values in set.

Eg: (1,2,2) median 2
(2,2,2) median 2

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Re: Is the standard deviation of set Q equal to 0?  [#permalink]

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02 Aug 2014, 08:39
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Is the standard deviation of set Q equal to 0?

(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q. Since mean = greatest, then Q consists of all identical elements. This implies that the standard deviation is 0 (the standard deviation of a set is zero if and only the set consists of identical numbers). Sufficient.

(2) The median of set Q is equal to the greatest number in Q. Clearly insufficient: If Q = {1}, then SD = 0, but if Q = {1, 2, 2}, then SD > 0. Not sufficient.

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Re: Is the standard deviation of set Q equal to 0?  [#permalink]

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02 Aug 2014, 08:39
Bunuel wrote:
Is the standard deviation of set Q equal to 0?

(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q. Since mean = greatest, then Q consists of all identical elements. This implies that the standard deviation is 0 (the standard deviation of a set is zero if and only the set consists of identical numbers). Sufficient.

(2) The median of set Q is equal to the greatest number in Q. Clearly insufficient: If Q = {1}, then SD = 0, but if Q = {1, 2, 2}, then SD > 0. Not sufficient.

Check other Standard Deviation Questions in our Special Questions Directory.

Hope this helps.
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Re: Is the standard deviation of set Q equal to 0?  [#permalink]

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02 Oct 2018, 03:59
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Re: Is the standard deviation of set Q equal to 0?   [#permalink] 02 Oct 2018, 03:59
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