Which of the following sets of numbers has the greatest standard devia

SD of A to D in ascending order.

D<A=B<C

Now C is equally spaced and [x-avg(x)]^2=4+2+4=8

Avg of E is 21.5 and [x-avg(x)]^2=2.25+0.25+1=3.5

Answer : C

need to compare only option C and E
For C, Range is 4
For E ranger is only 2.5 so obvisouly it will have less SD

So anwer is C

Standard deviation is the deviation from the mean.
Mean for set C is 0 and hence it's values have highest deviation from the mean in this set.
Hence option (C).

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MAGOOSH OFFICIAL SOLUTION:

FAQ: What about answer choice (E)?

This is definitely the trickiest of the wrong answers. If you chose (E), you're not alone!

Since these lists of numbers are very short and there's the same number of elements in each--only three in each answer choice--let's use the quick way to compare SDs: compare the ranges.

The range of (C) is 2 - (-2) = 4.
The range of (E) is 22.5 - 20 = 2.5.
Since the range of E is smaller (and these are such small lists), it's pretty safe to assume that the SD is also smaller

But if that's not convincing enough, we can find the exact SD of (E)

First, what's the mean of those three numbers?
(20 + 22 + 22.5) / 3
64.5 / 3
21.5

Next, how far away is each number from the mean?

20 is 1.5 away from 21.5
22 is .5 away from 21.5
22.5 is 1 away from 21.5
This means the standard deviation is the average of .5, 1, and 1.5, which means SD = 1.

This is smaller than the average of 2, 0, and 2 from answer choice (C), which would be 4/3 = 1.33.

Dear AMsac123,

With all due respect, you have pressed to have me ask your question, and it's far from clear to me that you read the blog article to which I linked. If you understood everything in that blog, you would have answered your own question.

As general rule, sets with larger ranges tend to have larger standard deviations. If we were to measure the range & S.D. for every single set that, for example, has ever appeared on the GMAT, I would expect the range and S.D. to be highly correlated. Nevertheless, as always, correlation is only a statement about a general pattern, and not a statement that is true in the granular sense. Thus, if Set A has a larger range than Set B, we can't necessarily say anything about the standard deviations of these two sets.

Consider these two example sets.
Set A = {40, 40, 40, 40, 40, 60, 60, 60, 60, 60} ==> mean = median = 50, range = 20
Set B = {35, 50, 50, 50, 50, 50, 50, 50, 50, 65} ==> mean = median = 50, range = 30

Set B clearly has a much larger range. But look at how the numbers are distributed. All the numbers in Set A are at the extreme values, 10 units away from the mean, so S.D. = 10. Meanwhile, 8/10 of the numbers in Set B are at the mean, with a deviation of zero. Thus, it appears that Set B will have a much smaller S.D.

In Set A, every deviation has an absolute value of 10, so S.D. = 10
In Set B, one deviation is -15, one is +15, and other eight are zero. Sum of square deviations = 225 + 225 = 450. Average of square deviations = 45. S.D. = \(\sqrt{45}\) = \(3\sqrt{5}\) = 6.7082

Thus, Set B has a larger ranger and a smaller S.D.

Once again, I would strongly recommend reading this blog if you haven't do so already.
Standard Deviation on the GMAT
As a general rule, the way you show respect to an expert for providing help is to acknowledge explicitly everything you learned from what they already shared. If everything they shared has not answered your question, it's fine to present that as well, but to insist on what you want to know and to disregard everything else an expert tells you is relevant is disrespectful.

Does all this make sense?
Mike

How about this for The OG 2017 PS 47 qn? Same logic if u apply how will we get it?

mikemcgarry Bunuel Magoosh

Thanks Mike I understand that > i was just trying to corelate the concepts in the two questions and how it can be applied > i wanted to check if the thinking is correct or if i am missing anything. All im checking is if the above snipet of lowest range= lowest std is a general rule and can be applied to all such questions?

hi mikemcgarry waiting patiently for ur reply

Thanks Mike. I dint mean to be respectful. Just wanted to get a clarity if there is a corelation between range and STD. I am sorry if you felt that way ! Thanks again

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