Source: Revised GRE PDF 2nd Ed. Section 5; #8 (p. 77)


The frequency distributions shown above represent two groups

The frequency distributions shown above represent two groups of data. Each of the data values is a multiple of 10. Quantity A: The standard deviation of distribution A Quantity B: The standard deviation of distribution B Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

3 Explanations


Riva Mitra

how did you calculate the average so fast?

Jun 20, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Good question!

Mike did this by diving the bars into groups. Let's consider distribution A.

Here, we can see that the middle is 30. So let's see if we can "pair up" the other bars so that the pairs give us an average of 30.

Well, we know that 10+50 = 60, and so the average of 10 and 50 is 30. So we can pair up 10 and 50, and the average of those is 30.

We can also pair up 20 and 40. Those add up to 60, so the average of 20 and 40 is 30.

Now we've considered all of the bars, except for the one in the middle. The average of 30 is 30. So all the numbers, if we pair them up correctly, give us an average of 30. Since all the numbers have now been accounted for, we know that the average of the entire distribution is 30.

The same method can be used for distribution B.

I hope this helps, Riva! :)


Jul 6, 2017 • Reply

Riva Mitra

Thanks Sam! Just one more question; this method applies due to the reason that there is an equal number of 10s and 50s for example. But what if the number of 50's and 10s weren't the same, and also if the # of 40s and 20s frequency was not the same. How would deduce the SD ?

Jul 6, 2017 • Reply

Riva Mitra

Thank you btw :)

Jul 6, 2017 • Reply

, Magoosh Tutor

Hi Riva, sorry for the delay in response! The purpose of this question is to find a pattern in the graphs and recognize the standard deviation based on this pattern. If we didn't have this pattern (same number of 50s and 10s, same number of 40s and 20s), then we would have to use the standard deviation formula, which is time-consuming and difficult ( . The GRE is interested in your critical thinking abilities, not whether or now you can punch numbers into a formula and calculator, so they will never ask you to calculate the SD like that. SD questions will test your understanding of the concepts of SD, not the specific calculation of it! Like Chris says in the video: if you don't immediately recognize the pattern here, you should move on and come back to this question later :-)

Sep 1, 2017 • Reply


Robert Paul

I picked "B" simply because there was more variability in the distribution of data in B, regardless of what their means were. Not sure if that way of looking at it will always result in a correct answer.

Sep 18, 2014 • Comment


Gravatar Chris Lele, Magoosh Tutor

Sep 27, 2012 • Comment

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