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If m is the arithmetic mean (average) of 4 integers a, b, c, and d and

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If m is the arithmetic mean (average) of 4 integers a, b, c, and d and [#permalink]

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If m is the arithmetic mean (average) of 4 integers a, b, c, and d and s is the standard deviation of the 4 integers, then is s > 0?

(1) m > a
(2) a + b + c + d = 0
[Reveal] Spoiler: OA

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Re: If m is the arithmetic mean (average) of 4 integers a, b, c, and d and [#permalink]

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Standard deviation can either be zero or a positive number. It can never be a be a negative number (Look up the formula, it's the sum of squares). A zero standard deviation implies that all the numbers in the set are the same (as the distance between them is zero). And a positive number standard deviation tells us that the numbers are not the same.

The questions asks us if s > 0. We can answer this just by knowing whether all the numbers in the sets are the same or not.

Statement (1) tells us that the number 'a' is less than the average 'm' of the set. From this piece of information, we know that all the numbers in the set are not the same. (if all the numbers in the set had been the same, then every number would have been equal to the average.) Hence the standard deviation is going to be greater than zero.

Statement (1) is sufficient

Statement (2) tells us the sum of all the numbers in the set is equal to zero. This can be the case if all the numbers were zero (hence all were same) or this can also be the case if a=b=2 and c=d= -2 (numbers are not same).

Statement (2) is insufficient

imo, the correct answer is (A)
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Re: If m is the arithmetic mean (average) of 4 integers a, b, c, and d and [#permalink]

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New post 12 Mar 2016, 05:45
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m is the arithmetic mean (average) of 4 integers a, b, c, and d and s is the standard deviation of the 4 integers, then is s > 0?

(1) m > a
(2) a + b + c + d = 0


When you modify the original condition, the question s>0? means if there is any other number since all the number are the same when s=0. For 1), from m>a, (a+b+c+d)/4>a, a+b+c+d>4a, b+c+d>3a. From b+c+d>a+a+a, it means that at least one pair is different in a,b,c,d, which is yes and sufficient.
Therefore, the answer is A.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If m is the arithmetic mean (average) of 4 integers a, b, c, and d and [#permalink]

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Re: If m is the arithmetic mean (average) of 4 integers a, b, c, and d and   [#permalink] 25 Apr 2017, 07:12
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