Takeaway from OG Green pg 190 ex 107

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GMATCHPOINT: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Oct 08, 2008 12:50 pm

by GMATCHPOINT » Tue Oct 21, 2008 1:33 pm

Can I assume that for a certain set of N numbers, with numbers listed in increasing order and all numbers N being consecutive and evenly spaced, the average of the set and the median will ALWAYS be equal?

Just trying to get a takeaway from the following ex from og:

For a certain set of N numbers, where N>1, is the average equal to the median?
(1) if the N numbers in the set are listed in increasing order, then the difference between any pair of successive number in the set is 2.
(2) The range of the N numbers in the set is 2(n-1)

I know this is basic, but am terrible with statistics...

cheers!

Source: Beat The GMAT — Data Sufficiency | Tue Oct 21, 2008 1:33 pm

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Re: Takeaway from OG Green pg 190 ex 107

by Ian Stewart » Wed Oct 22, 2008 6:14 am

GMATCHPOINT wrote:Can I assume that for a certain set of N numbers, with numbers listed in increasing order and all numbers N being consecutive and evenly spaced, the average of the set and the median will ALWAYS be equal?

Yes, in any 'evenly spaced' set, the median and the average are always equal -- and, in fact, they are both equal to the average of the smallest and largest elements in the set. So if you have this evenly spaced set, increasing by 7:

{10, 17, 24, 31, 38, ... 703, 710, 717, 724}

you can find the average and the median quickly: it's equal to the average of 724 and 10 (which is 367).

This is a very important fact in statistics, but do be sure to use it correctly - if your set is not evenly spaced, it will often be true that the median and mean are different, of course.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

GMATCHPOINT: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Oct 08, 2008 12:50 pm

by GMATCHPOINT » Wed Oct 22, 2008 1:48 pm

thanks Ian!
one more takeaway from og exercises. I am following Ron`s advice and trying to get generalized "takeaways" from most of the problems from og and hopefully be able to apply to other problems during the real gmat.

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