Data Sufficiency

goelmohit2002 wrote: https://www.beatthegmat.com/in-which-ran ... tml#184015

or do u guys think that:

a) deviation is something different than standard deviation...then how to calculate the same and reach to the answer.

b) or u guys think that the OA at the above thread is incorrect ?

Kindly share your opinion please.

First, I'm curious where these questions are from, since they're testing things you don't need to know about on the GMAT. And the question linked above, for example, makes no mathematical sense.

m&m wrote:no need to get into SD formula - 1SD on either side of mean gives a range of 68% of the items in the set.

This is almost *never* true. As Dana pointed out above, this is true for "normally distributed" sets, but I've never seen a normally distributed set in a GMAT question.

goelmohit2002 wrote:Just one thing to ask which is the correct relation to remember:
a) R >= SD
or b) R > SD

The range and the standard deviation can be equal, when both are equal to zero (i.e. when all elements of your set are the same). I've never seen a real GMAT question on which you would need to know that the SD is always less than or equal to the range, and I've certainly never seen a question that requires you to know anything more than that. It's not at all easy to prove that 2SD <= R, and that's definitely not something the GMAT will ever test.

mehravikas wrote:With that we should remember that SD is directly proportional to the range. If the range of a set changes, SD will change accordingly.

Standard Deviation is not directly proportional to the range. One set can have a larger range and a smaller standard deviation than another - consider these two sets, for example:

{0,50,50,50,50,50,50,50,50,50,100}

{1,1,1,1,1,50,99,99,99,99,99}

The second set has a smaller range and larger standard deviation than the first.

you will not have to know anything like this on the exam.

actually, unless the test authors do a complete about-face on this issue, you'll NEVER need to worry about the NUMERICAL VALUE of the standard deviation, AT ALL.

there have been several problems (4-6, i can't remember the exact number) that have given a numerical value to the standard deviation.
in ALL of these problems, the concept of standard deviation was completely irrelevant. you could take "standard deviation" and replace it with "pink flamingo", and the problem wouldn't change.
see here for an example:
https://www.manhattangmat.com/forums/post17297.html

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the only thing you'll have to know about the numerical value of the standard deviation is how to REDUCE or INCREASE it.
specifically, you can reduce it, guaranteed, by adding numbers that are closer to the mean than are any of the existing numbers.
you can increase it, guaranteed, by adding numbers that are farther from the mean than are any of the existing numbers.