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Is the standard deviation of set Q equal to 0?

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

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New post 02 Aug 2014, 05:49
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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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Re: Is the standard deviation of set Q equal to 0? [#permalink]

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New post 02 Aug 2014, 06:06
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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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New post 02 Aug 2014, 09:39
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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.

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

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New post 02 Aug 2014, 09:39
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.

Answer: A.


Check other Standard Deviation Questions in our Special Questions Directory.

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

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New post 29 Mar 2017, 11:11
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Re: Is the standard deviation of set Q equal to 0?   [#permalink] 29 Mar 2017, 11:11
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