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What is SD of given set of numbers whose average is 5?

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Source: — Data Sufficiency |

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by [email protected] » Sun Jan 24, 2016 2:51 pm
Hi sachin_yadav,

What is the source of this question? I ask because the 'design' of this question is incorrect (the two Facts CANNOT BOTH be sufficient while giving different answers).

We're told that the average of a group of numbers is 5. We're asked for the Standard Deviation of the group.

1) None of the numbers are greater than this Average

The ONLY way that this can occur is if ALL of the numbers in the set are the SAME number. Thus, while we don't know how many numbers are in the set, we do know that they are all 5s. By extension, the SD = 0
Fact 1 is SUFFICIENT.

2) The Standard deviation is 5 when value of each of the given number is increased by 7

This Fact doesn't tell us what the numbers are, BUT if we increase EACH number by 7, then the Stand Deviation would still the SAME. By extension, the SD = 5
Fact 2 is SUFFICIENT.

This would make the answer D, but the GMAT does NOT create its DS questions in this way. The SD CANNOT be 0 and 5.

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by sachin_yadav » Mon Jan 25, 2016 9:58 am
Hi Rich,

Thanks for your reply. I got this question from GMAT club while i was practising. I totally agree that both statements are contradicting each other in answers. However, it's a good question because it tests on concepts.
I am a bit weak in Standard deviation concepts.

Regards
Sachin
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by Brent@GMATPrepNow » Mon Jan 25, 2016 10:40 am
sachin_yadav wrote: I am a bit weak in Standard deviation concepts.

Regards
Sachin
It's important to note that, for the purposes of the GMAT, we need not involve the actual standard deviation. Instead, it's sufficient to think of Standard Deviation as the Average Distance from the Mean. This is a convenient way to handle most standard deviation questions on the GMAT.

Here are two free videos that cover everything you need to know about standard deviation:
- https://www.gmatprepnow.com/module/gmat- ... ics?id=806
- https://www.gmatprepnow.com/module/gmat- ... ics?id=809

Here are a few more practice questions to try:
- https://www.beatthegmat.com/standard-dev ... 74384.html
- https://www.beatthegmat.com/standard-dev ... 69584.html
- https://www.beatthegmat.com/range-and-sd-t89159.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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