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# If the average (arithmetic mean) of 7 numbers is 21, what is the stand

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Math Revolution GMAT Instructor
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If the average (arithmetic mean) of 7 numbers is 21, what is the stand  [#permalink]

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15 Aug 2017, 01:30
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If the average (arithmetic mean) of 7 numbers is 21, what is the standard deviation of the numbers?

1) The smallest number of them is 21
2) The greatest number of them is 21

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Re: If the average (arithmetic mean) of 7 numbers is 21, what is the stand  [#permalink]

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15 Aug 2017, 02:20
1
(1) If the smallest number is 21, then any other number in the set should be at least 21.
Average number would be equal to 21 only if all the numbers in the set would be equal to 21. Thus it means that SD is zero.
SUFF.
(2) If the highest number is 21, then applying same the same logic as statement 1, any other number in the set should be equal to 21 to make the average equal to 21. If any number would be less, then average will be less than 21. Thus again SD is zero and statement 2 is SUFF.

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Re: If the average (arithmetic mean) of 7 numbers is 21, what is the stand  [#permalink]

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17 Aug 2017, 00:51
=>Condition 1)
Since the minimum number and the average are same, all numbers should be 21.

Condition 2)
Since the maximum number and the average are same, all numbers should be 21.

Ans: D
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Re: If the average (arithmetic mean) of 7 numbers is 21, what is the stand  [#permalink]

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17 Aug 2017, 00:59
The smallest number is 21. Of the other three numbers if any one is greater than 21 then one of the numbers is less than 21 since the avearge is 21. For eg 19,21,23. If the largest is 21 then all the numbers have to be 21 for the same reason. So the answer is D.
Re: If the average (arithmetic mean) of 7 numbers is 21, what is the stand   [#permalink] 17 Aug 2017, 00:59
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