Many quake in their boots when they hear that there will be Statistics covered on the GRE. They run to their college stats textbooks, dust off the cover, roll up their sleeves, and start computing the standard deviations of a list of twenty, three-digit numbers. Stop, if this in anyway describes you.
The Statistics on the GRE is much simpler, and does not test your aptitude at crunching numbers as much as it does your ability to think about Statistics. That is you will rely more in intuition than computation on statistics questions on the GRE. You shouldn’t be so worried about how many statistics questions there are on the GRE, anyway.
To illustrate take a look at the following question.
1- The standard deviation on a test was 12 points, and the mean was 70. If student X scored 95 points, then student X scored higher than approximately what percent of students?
- 2%
- 13%
- 48%
- 96%
- 98%
Answering this question correctly requires understanding standard distribution (that refers to the distribution of scores along the familiar bell-curve). To understand how standard deviation relates to the bell-curve take a look below:
1 Standard Deviation Above = 34%
1 Standard Deviation Below = 34%
2 Standard Deviations Above = 13.5%
2 Standard Deviations Below = 13.5%
3 Standard Deviations Above = 2%
3 Standard Deviations Below = 2%
In the problem above, 34% of students scored between 70 and 82. Likewise, 34% of students scored between 58 and 70. This symmetry is very important, and you will notice that the bell curve is symmetrical (or even) on both sides. So, given a large enough sample size, the number of students who scored three standard deviations below the average of 70 (34) is the same as the number who scored three standard deviations above the average (106).
Returning to the actual question, we want to find how many standard deviations above the average a score 95 of points is: 95 – 70 = 25, which is a tiny bit more than two standard deviations. The question is asking for an approximation, so we can round down 25 to 24.
Looking at table above, we can see that two standard deviations above the norm is better than 34% + 13.5%. The trick here is to not forget to account for the left side of the bell-curve, which is 50% (after all, half the score are on the left side and the other half on the right side—don’t forget the symmetry of the bell-curve).
That gives us a total of 50% + 47.5 = 97.5, which approximates to (E) 98%.
Let’s try another problem.
2. The reaction time of 1000 Rhesus monkeys was measured. The average time it took the monkeys to respond to a quickly moving object in their visual fields was .135 seconds, with a standard deviation of .021 seconds. If one of the geriatric monkeys had a reaction time of .205 seconds, then that monkey’s reaction time is how many standard deviations from the mean?
- 0 – 1 standard deviations
- 1 – 2 standard deviations
- 2 – 3 standard deviations
- 3 – 4 standard deviations
- 4 – 5 standard deviations
This is exactly the sort of daunting problem that the GRE likes to throw at you. Believe it or not, there is very little math involved. Again, you want to rely on intuition more than math.
.205 – .135 = .07. If the standard deviation is .021, we can determine the number of standard deviations the monkey’s reaction time is from the mean: .07/.021, which equals approximately 3.4. Therefore (D) – the geriatric monkey’s reaction time is 3 – 4 standard deviations from the mean.
Takeaway
To do well on statistics questions on the GRE, you have to rely more on intuition than on number crunching. Having a strong sense of standard distribution and how standard deviation relates to standard distribution will help you immeasurably.
Hi Chris,
For all our sakes, I’m divulging this : when I first passed my GRE last July, I got a question that required computing a standard deviation. Well, almost. It gave you the standard deviation of three numbers, and asked for its new value when the numbers were changed in a certain manner.
Now the question may have been part of the experimental section or could’ve been solved without otherwise knowing the formula. I still wonder how though.
So Chris could you please weigh in on the matter and explain how I should’ve come up with the answer without using the formula?
Thanks!
Thanks for divulging
I really can’t say for sure, but I’d be surprised if the GRE had a question in which the only way one could reliably solve it is by using the Standard Deviation formula. Inferential thinking is typically also rewarded. That is, SD on the GRE is about having this sense of what it means for any given set of numbers to have a greater standard deviation than another set.
For instance, if I have (3, 4, 5, 7) and (2,3,4,6.1), the standard deviation is greater in the second set (notice the difference between 6.1 – 4 is greater than that of 5 and 3). I am sure the problem you saw was more complex, but again the inferential approach would have been successful as well.
All this said, I think it safe to memorize the SD formula – just in case.
Let me know if you have any more questions…and to think of it, all of this has inspired a blog post: How to solve Standard Deviation without using the big, nasty formula. Look for it soon
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Looking forward to it then
Hey Chris,
I’m stuck on the first problem. I understand every step until we account for the left side of the bell curve. If the bell curve is symmetrical, then shouldn’t it be 47.5+47.5? Where did the 50% come from?
Hi SB,
It is indeed symmetrical, 47.5% on either side of the mean gives us a 95% range.
In this problem, however, the entire left half of the curve represents test scores below the average. Therefore, if we get a test score that is 2 standard deviations above the mean, it will be better than all the test scores below it. This includes the scores between our score and the average AND all of the scores below the average (not just 47.5% of the scores below the average).
If we wanted to know what percent of score were within 2 standard deviations of the mean in either direction, then we would take 47.5% on each side. In this case we’re just concerned with everything below a certain value.
I hope that helps!
Thanks Jonah
.
Very clearly explained. I should have probably been clearer where the 50% came from.
Thanks again!
Sorry for the confusion
. Since we are accounting for all the scores below 70 (the mean), that number represents half of all scores. Hence the 50%. Also check out Jonah’s comment below. I think he does a good job of explaining the concept 
.
Hey Chris!
Thanks for your previous reply. Please answer the following:-
1) I am done vit std deviation too, its relation with bell curve(d 3 no’s viz 68,95,99), the concept of probability distribution,freq distribution,etc. Which part I havnt touchd yet?
2) Also, what is the difficulty level of Manhattan GMAT quants, compared to actual GRE?
3) Which has an equal level? Manhattan GRE verbal or which verbal material?
Thank-you
1) As far as the bell curve goes that is sufficient.
2) MGMAT quants are much more difficult than actual GRE questions.
3) MGRE tends to be pretty difficult for verbal. It’s comparable to test.
Hope that helps!
Hey Chris!
How you doing?
Please tell me what concepts pertaining to Data analysis should be studied for revised GRE. I am done with the following:-
1) Mean,mode,median, concept of random variable.
2) Normal distribution(Bell curve)
3) quartiles,interquartile range,percentile.
What more should be learnt?
Thanks!
You are doing a great job
Hi Deepak,
Good question! I think you pretty much covered everything except Standard Deviation. Otherwise, your list is comprehensive
.
Hi Chris,
As the theme of the week goes (ETS PAPER BASED TEST) I thought to include a question from new version of paper based.test by ETS:
Section 5 question 8:-
Thefrequencydistributionsshownaboverepresenttwogroupsofdata.Eachofthedata valuesisamultipleof10.
QuantityA 8.Thestandarddeviationof distributionA
QuantityB Thestandarddeviationof distributionB
It may not be clear from the description and moreover there weee two bar graph involved which I am unable to paste here
Thanks
Hi Aman,
I’ve actually already recorded this video and it should be up soon. Doing such a graph-based problem without the graph is very difficult, so look for the questions on youtube soon!
Hi Chris,
What abt calculating standard deviations? Would we be asked to do that?
TnR
Prem
Prem,
Only in rare instances – it seems the GRE is more focused on testing one’s sense of standard deviation vs. one’s ability to actually compute it.
well explained
Thank you!
Hey Chris,
Would the GRE really phrase a question like this? We learned in my college Statistics class that just because one value is “better” (in this case faster) doesn’t mean that the answer has to be “below the mean”. It’s perfectly plausible in statistics to have higher numbers mean “worse” results but still refer to them as being “above the mean”. I think somebody who calculated the answer as 3-4 standard deviations above the mean would have a legitimate gripe if the answer was marked incorrect.
Ooh…I was thinking about that when I was writing the question and wanted to make sure it wasn’t ambiguous… but you’re right. ‘Better’ is arbitrary. I will make the changes. Thanks for your sharp eye!
Typo or careless error? In the monkey problem, the reaction time is .215, but when you solved the problem, you used .205.
I feel better about myself now, seeing that even Chris makes mistakes sometimes!
Yes, I am human
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I’ll make the changes. Thanks for catching the oversight!