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std deviation !

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std deviation !

by francoisph » Wed Jun 16, 2010 6:17 am
1 - 18, 25, 25, 25, 26, 64
2 - 32, 32, 32, 32, 32, 32
3 - 37, 38, 39, 40, 41, 42

Which of the following correctly list the data sets above in order of least to greatest standard deviation

A - 1, 2, 3
B - 1, 3, 2
C - 2, 1, 3
D - 2, 3, 1
E - 3, 2, 1

should we calculate all std deviation? or is it possible to resolve quickly?
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by krazy800 » Wed Jun 16, 2010 6:25 am
francoisph wrote:1 - 18, 25, 25, 25, 26, 64
2 - 32, 32, 32, 32, 32, 32
3 - 37, 38, 39, 40, 41, 42

Which of the following correctly list the data sets above in order of least to greatest standard deviation

A - 1, 2, 3
B - 1, 3, 2
C - 2, 1, 3
D - 2, 3, 1
E - 3, 2, 1

should we calculate all std deviation? or is it possible to resolve quickly?
No you don't need to calculate the std deviation.


All you need to do is calculate the mean of each mumber series

Then take a look at difference of the values from the mean in each set


The set which has values with minimal difference from the mean has minimum standard deviation.

Now try that on the sets 1, 2, 3

ur order should be 2,3,1

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by Rich@VeritasPrep » Wed Jun 16, 2010 6:37 am
Hey guys,

In actuality, you don't even need to calculate the mean of the sets. As krazy800 correctly pointed out, you also don't need to calculate std deviation. The GMAT does not test in-depth mathematical knowledge of std deviation. It just tests std deviation as a concept.

It's true that all you need to know is that std deviation represents how far from the mean the numbers are spaced. But most of the time (if not ALL of the time), you can figure this out without any calculation:

1 - 18, 25, 25, 25, 26, 64
2 - 32, 32, 32, 32, 32, 32
3 - 37, 38, 39, 40, 41, 42

The most obvious is list 2. Because every element is the same, you know immediately that this element is the mean. Since every element equals the mean, the std deviation is 0.

You should be able to identify the mean of list 3 just by eyeballing it. The numbers are equally spaced, so the mean is the average of the middle two terms (i.e. 39.5). This will result in some std deviation, but not much.

The dead giveaway in list 1 is the 64. You have four numbers in the middle that are very close together. You have an 18, which is a little bit more distant. But then, the 64 is WAY far away from the rest. List 1's std deviation will thus be much greater than those of the other two lists.

So in short, you have lists with zero std deviation, a little std deviation, and a lot more std deviation, respectively. That's all you need. No calculations necessary!
Rich Zwelling
GMAT Instructor, Veritas Prep
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by francoisph » Wed Jun 16, 2010 7:10 am
thks indeed
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