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Is the standard deviation of numbers x, y, and z, positive?

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Is the standard deviation of numbers x, y, and z, positive?  [#permalink]

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New post 18 Jul 2018, 03:38
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D
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  55% (hard)

Question Stats:

56% (01:14) correct 44% (01:26) wrong based on 101 sessions

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Re: Is the standard deviation of numbers x, y, and z, positive?  [#permalink]

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New post 18 Jul 2018, 04:13
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the standard deviation can be positive or 0, never negative. It will be 0 only when each element is same

Is the standard deviation of numbers x, y, and z, positive?

(1) The average (arithmetic mean) of x, y, and z, is less than x
this means the elements are not the same, so there is some dispersion and it is always positive
Sufficient
(2) The median of x, y, and z, is greater than z
Same again. All elements are not the same.
SD is positive
Sufficient

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Re: Is the standard deviation of numbers x, y, and z, positive?  [#permalink]

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New post 18 Jul 2018, 11:34
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Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION



Is the standard deviation of numbers x, y, and z, positive?

(1) The average (arithmetic mean) of x, y, and z, is less than x
(2) The median of x, y, and z, is greater than z


The SD will always be Greater Than or Equal to 0. It can never be Negative.

{Background Information:
Case 1: SD=0
This means that all the elements of the set are the same.

Case 2: SD>0
This means that the all the elements of the set are not equal.}

Getting back to the Question:
Statement 1:(1) The average (arithmetic mean) of x, y, and z, is less than x
This means that atleast 1 element of the 3 is different than the rest 2.
Therefore, the SD >0.

Statement 2: The median of x, y, and z, is greater than z
This means that at least z is different than x or y
This implies that atleast on e element is different in the set.
Therefore, SD >0.

Hence, the answer is D.

Please Note that the probability of GMAT asking test takers to calculate the value of SD is very low. However, it does asks questions on the basics of SD.
This is a very good question testing the basics of GMAT.
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Re: Is the standard deviation of numbers x, y, and z, positive?  [#permalink]

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New post 24 Dec 2018, 01:51
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Re: Is the standard deviation of numbers x, y, and z, positive?  [#permalink]

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New post 30 Dec 2018, 01:14
Trick here is to remember that standard deviation of a set can only be positive or 0. Standard deviation will be 0 if all elements are the same.

1) Given that average of x, y and z is less than x means that there is at least one number that is less than x. This means that all elements are not equal. Hence, standard deviation is not 0. Thus it has to be positive. Hence, sufficient

2) Given that median of the set is greater than z means that z is the smallest number and that it is different from the other two numbers. The latter is true because if any of the other two numbers was equal to z, median would have been equal to z, which is not the case. Thus, all elements are not equal. Hence, standard deviation is not 0. Thus it has to be positive. Hence, sufficient

Hence, answer is D
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Re: Is the standard deviation of numbers x, y, and z, positive?   [#permalink] 30 Dec 2018, 01:14
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