Need help with this DS question!

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rishianand7: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Tue Mar 05, 2013 10:18 pm; Thanked: 4 times

by rishianand7 » Wed Apr 24, 2013 6:37 am

List M (not shown) consists of 8 different integers, each of which is in the list shown below:
4,6,8,10,12,14,16,18,20,22
What is the SD of the numbers in the list M?

1) The average (Arithmetic Mean) of the numbers in the list M is equal to the average of the numbers in the list shown
2) List M does not contain 22

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Source: Beat The GMAT — Ask the Test Maker | Wed Apr 24, 2013 6:37 am

Ben.Miller@ApexGMAT: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Apr 24, 2013 6:14 amFollowed by: 2 members; Location: Global; Thanked: 8 times; GMAT Score:790

by Ben.Miller@ApexGMAT » Wed Apr 24, 2013 6:55 am

The standard deviation is the same as the average OF the average distance from the mean.

To find the standard deviation, we need the mean, and the average distance of all points from the mean. We can certainly get this from having all members of the set, but that is NOT necessary.

1) provides the mean. It DOES NOT provide the distribution of the numbers.
INSUFFICIENT

2) does NOT provide the mean, or the distribution of numbers.
INSUFFICIENT

Putting them together, however, may yield the distribution.

We know from 1) that the mean is 13. Since each number can only appear once, and we need 4 numbers above the mean, we know that 14, 16, 18, and 20 are in the set. To get an average of 13, they must be complemented by 6, 8, 10, 12, so we now have the full set and can compute the Standard Deviation.

So out answer is C.

Note, we don't need to outline the entire set, just get to the point where we REALIZE that we can narrow down to the actual set.

Ben[/i]

Ben Miller
Senior Instructor
Chief Curriculum Developer
ApexGMAT
[email protected]

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rishianand7: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Tue Mar 05, 2013 10:18 pm; Thanked: 4 times

by rishianand7 » Wed Apr 24, 2013 10:45 am

Hi,

Thanks for the solution. I have one doubt though.
Why can each number only appear once and 4 numbers need to be above the mean (13)?

Regards,
Rishi

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OfficialGMAT: Official Company Rep; Posts: 669; Joined: Tue Jun 12, 2012 9:06 pmFollowed by: 270 members; Location: Washington DC; Thanked: 143 times; GMAT Score:800

by OfficialGMAT » Wed Apr 24, 2013 5:27 pm

Hi, all! This thread is for questions for the makers of the GMAT exam. Unfortunately we cannot help you with answers to specific practice questions. Please re-post this to one of the main threads. Thank you!

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