standard deviation data sufficiency

[bgussin]

If the standard deviation of Set Y is 4, what is the range of scores that fall within one standard deviation?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.

The answer according to the MGMAT is B. I dont understand why either is needed (which would mean each is enough since they aren't needed). If the standard deviation of a set is 4, then the range within that SD is always 8, no matter what. You go four to the left and four to the right, the difference is 8, you dont need to know the mean at all. Am I missing something?

[sd]

(1) Insufficient. Median will not tell us anything useful in this case.

(2) Sufficient We are told mean is 6. And the standard deviation is 4. Therefore,
lowest score of the first standard deviation is 6-4 =2
highest score of the first standard deviation is 6+4 = 10

Hence range of scores that fall within first standard deviation is 10 -2 = 8.

bgussin, but I understand your point. You actually dont need the mean....lets see if anybody else has a better answer.

[mxs2009]

I think you'll chuckle after reading this one.

It's true, the range will always be 8, but the question is asking for the range of scores.

Only B gives us that [2,10]

[RonPurewal]

i side with the first poster on this one. we need to re-word this problem.

IN STATISTICS, the word "range" is ALWAYS taken to mean "difference between lowest and highest", unless the problem statement clearly and specifically defines it otherwise.

therefore, yeah, this isn't an acceptable problem, since the answer to the problem in traditional statistics terminology (range = 8) can be deduced from the problem statement alone, without using either of the statements.

i'll submit this for revision.

[hiokitsutomu]

Is the standard deviation of Set Y(2,6,10) 4?

Isn't is

√(((10-6)^2+(2-6)^2))/3)=√32/3 ?


I might be confused about the definition between "standard deviation" and "deviation".

For me the answer looks like the solution for "deviation", not "standard deviation".

Pls someone help me.

[RonPurewal]

The problem is asking for a range. I.e., top number minus bottom number. (This is the original issue with the wording.)

If the problem said just "within one standard deviation", then that's another problem, too: "Within one standard deviation" of what, exactly?
Presumably we're referring to the mean of the distribution, but, in that case, it's absolutely obligatory to say "within one SD of the mean".

In any case, this problem is no longer active in our database.

[RonPurewal]

There's an updated version of the problem in our database:
If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?
Statements 1 and 2 are the same.

This problem has neither of the issues discussed above, and its answer is unequivocally B.

[RonPurewal]

Is the standard deviation of Set Y(2,6,10) 4?

Isn't is

√(((10-6)^2+(2-6)^2))/3)=√32/3 ?

Something like that. (Whole truth: If I needed this formula, I'd have to look it up.)

But it's immaterial, because you will NEVER, EVER, EVER need to calculate a standard deviation on the GMAT.
Not ever. No way.

The entire point of the GMAT is for the problems NOT to depend on relatively obscure formulas.

[RonPurewal]

Here's a post in which I discuss what you do actually have to know about the standard deviation (not much at all):

post86007.html#p86007