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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, 02:38
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A
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D
E

Difficulty:

  45% (medium)

Question Stats:

52% (00:54) correct 48% (01:13) wrong based on 33 sessions

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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

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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, 03:13
1
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

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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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, 10:34
1
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? &nbs [#permalink] 18 Jul 2018, 10:34
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