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# Is the Standard Deviation of four positive numbers a, b, c, d greater

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Retired Moderator
Joined: 22 Aug 2013
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Is the Standard Deviation of four positive numbers a, b, c, d greater  [#permalink]

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13 Jan 2019, 22:20
3
00:00

Difficulty:

55% (hard)

Question Stats:

45% (01:05) correct 55% (01:16) wrong based on 39 sessions

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Is the Standard Deviation of four positive numbers a, b, c, d greater than 0?

(1) Average of a, b, c, d is greater than c but less than b.

(2) Product of a, b, c, d is less than 1.
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Re: Is the Standard Deviation of four positive numbers a, b, c, d greater  [#permalink]

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14 Jan 2019, 09:37
1
S.D is basically a non-negative value,
so it can be equal to zero if all the values in the set are equal
or it can be more than zero if there is different values.
so the question is asking whether the elements in the set are equal or not.

statement 1: clearly says that the values are different, because if they were identical, any element must be equal to the average.
so sufficient

statement 2:
the values of (a,b,c,d) can be ($$\frac{1}{2}$$,$$\frac{1}{2}$$,$$\frac{1}{2}$$,$$\frac{1}{2}$$) or ($$\frac{1}{2}$$,$$\frac{1}{3}$$,$$\frac{1}{5}$$,$$\frac{1}{7}$$). the product is still less than 1, so insufficient.

so A IMO.
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Thanks for Kudos
Re: Is the Standard Deviation of four positive numbers a, b, c, d greater   [#permalink] 14 Jan 2019, 09:37
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# Is the Standard Deviation of four positive numbers a, b, c, d greater

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