Standard Deviation on the GMAT: Do I have to know the formula?

Question

Does anyone know whether there are official GMAT questions that require one to know the precise formula for standard deviation? If so, then is Average Standard Deviation sufficient? I am aware of official questions that reference the "2,14,34" rule but none that require one to calculate SD, only to understand the concept itself as tested.

Concept #1: the actual numbers do not matter, only their distances from the mean. 
Concept #2: adding or subtracting the same amount from all numbers does not change the SD.
Concept #3: multiplying or dividing all numbers in the list by the same amount (except for one)  does  change the SD.

dabral  could you kindly confirm or deny?

KarishmaB · Answer

You are not required to calculate the actual SD so knowing the formula isn't critical. That said, it is good to know the formula because then you can easily figure out the concepts you have discussed above. You can easily figure out how SD will/will not change if each element is added/multiplied etc by the same number. Rather than learning every concept, just knowing the formula will help you figure out these and other concepts. Here are some discussions on SD: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/06 ... deviation/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/06 ... n-part-ii/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/06 ... questions/ My next week's post will discuss SD too - how to compare SDs of sets which look similar.

dabral · Answer

Hi Brian,

I will add to the list you presented above. Please note that for the longest time the GMAT did not test these concepts.

1) You will be asked to apply the sample standard deviation formula to compute the standard deviation of a list of numbers. However, in these cases you will be given the formula and all you will need to do is to interpret the formula and the notations. Please see the attached image for an example from the official guide.

2) You will be expected to know the formula for standard deviation and also understand how it can be manipulated and rewritten in the form that is called the "computational formula" for standard deviation. You can expect this on the hardest problems on the GMAT.

Cheers,
Dabral

mcelroytutoring · Answer

Thanks as always Dabral! According to GMAC, we are responsible for knowing the equation. But just to confirm, we don't currently know of any actual official questions that require one to know the formula for SD / computational formula, correct? If so, then do you have any examples?

I don't see the point in requiring my students to memorize the formula if we can't confirm that it actually shows up on tests. Maybe the students going for a perfect 51, but no one else. It's not so hard of a formula to memorize, but I would rather focus on core math principles (exponents, probability and combinatorics, number properties, factorials etc.) that will actually show up on the test frequently.

I understand the argument of "just because it hasn't shown up before on a released GMAT doesn't mean it won't show up on  your  GMAT." I've seen questions on actual GMATs that looked nothing like anything I have ever seen in my practice. I don't know whether or not these were experimental questions, but I suppose it's the GMAC's right to test any topic they tell us they are going to test. Hence, to play it safe, we should definitely memorize the formula. But I would love to see an example of an official question that requires it, if anyone has one.

DmitryFarberMPrep · Answer

Anecdotally, I've heard some higher-scoring students report that they are seeing multiple SD questions, but I can't confirm whether any of these questions required the formula. Also, I'd guess that if someone sees 2 or 3 SD questions, at least one is experimental.

dabral · Answer

Brian,

I am referring to actual GMAT questions on the test. I cannot disclose them because of GMAT's non-disclosure rules. As long as one can do the manipulation to go from the regular standard deviation expression to the computational formula version, then they will be fine on the exam.

Since Pearson Vue took over the GMAT beginning 2006, they have added several new topics that used to be absent in the old administration of the GMAT. Here are some examples of topics that come to my mind.

1) Equations of parabola and conditions for intersection in the coordinate plane.
2) Standard Deviation and range. 
3) Geometric series.
4) Greatest and least integer function, also called floor and ceiling function. In these cases, the definition is given, so no prior knowledge is required.

Additionally, GMAT writers also look at content from other sources and then use them on GMAT test. Here are some examples of AMC(American Math Competition) math questions that GMAT writers have used as inspiration in the last ten years.

My point here is that to differentiate scores at the upper end, the GMAT test designers need problems that are novel and that test problem solving skills, and one way they have been doing this is by expanding the pool of topics. There is only so much that GMAT writers can squeeze out of percent and distance/rate problems.

Cheers,
Dabral

deabas · Answer

I agree with Farmer from Manhattan GMAT.. Standard deviation questions are rarely in the actual GMAT exam.

Standard Deviation on the GMAT: Do I have to know the formula?

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