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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Mon Jul 21, 2014 6:01 am
For the purposes of the GMAT, it's sufficient to think of Standard Deviation as the Average Distance from the Mean. Here's what I mean:

Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18}
The mean of set A = 10 and the mean of set B = 10
How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.

Alternatively, let's examine the Average Distance from the Mean for each set.

Set A {7,9,10,14}
Mean = 10
7 is a distance of 3 from the mean of 10
9 is a distance of 1 from the mean of 10
10 is a distance of 0 from the mean of 10
14 is a distance of 4 from the mean of 10
So, the average distance from the mean = (3+1+0+4)/4 = 2

B {1,8,13,18}
Mean = 10
1 is a distance of 9 from the mean of 10
8 is a distance of 2 from the mean of 10
13 is a distance of 3 from the mean of 10
18 is a distance of 8 from the mean of 10
So, the average distance from the mean = (9+2+3+8)/4 = 5.5

IMPORTANT: I'm not saying that the Standard Deviation of set A equals 2, and I'm not saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).

What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A.
More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GMAT.

------------------------------
Quote:
Sets A,B and C are shown below.If number 100 is included in each of these sets, which of the following represents the correct ordering of the sets in terms of the absolute increase in their Standard Deviation, from largest to smallest?
A {30,50,70,90,110}
B {-20, -10,0,10,20}
C {30,35,40,45,50}

(A) A,C,B (B)A,B,C (c)C,A,B (d)B,A,C (e)B,C,A
So, for this question, we have:

Mean of set A = 70
Mean of set B = 0
Mean of set C = 40

100 is furthest away from the mean of 0 in set B, so this will cause the GREATEST change in standard deviation.
100 is next furthest away from the mean of 40 in set C, so this will cause the 2nd greatest change in standard deviation.
100 is closest to the mean of 70 in set A, so this will cause the LEAST change in standard deviation.

Cheers,
Brent

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Mon Jul 21, 2014 6:10 am
With Standard Deviation questions on the GMAT, you will never be asked to calculate the actual standard deviation, because that involves some complex computation. To actually calculate, we'd find the difference between each term and the mean, then square that, then find the average of all of those, and square root that. For reference: http://en.wikipedia.org/wiki/Standard_deviation#Basic_examples

The GMAT will never ask you to do that! The most that they can ask is that you understand that high SD means the data is spread out far from the mean, and a low SD means that most data is clustered closely around the mean. Whenever you see a SD question, just translate it as "how much is the data spread out?"

When you add 100 to each set, the further 100 is from the mean, the more it will "spread" the data out from the mean.

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Mon Jul 21, 2014 6:13 am

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Mon Jul 21, 2014 6:21 am
Here are a few more practice questions where we can apply the concept of "average distance from the mean" as an approximation for Standard Deviation:

http://www.beatthegmat.com/standard-deviation-more-than-s-t274384.html
http://www.beatthegmat.com/standard-deviation-t269584.html
http://www.beatthegmat.com/range-and-sd-t89159.html

Cheers,
Brent

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neha shekhawat Junior | Next Rank: 30 Posts
Joined
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Posted:
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Tue Aug 01, 2017 3:38 pm
Hey Brent,
I am confused with the language of this question ( the absolute increase in their Standard Deviation, from largest to smallest? )
Is this question asking to arrange the S.D of all set in descending order?
I totally understand the concept of S.D, and looking at the given set and their spread I can easily see that first set has largest S.D and last set has the least S.D.
So if this question is asking about arranging the S.D in descending order then it would have been a,b,c.
But this is not the answer.
what is absolute increase in this case?
As when we calculate S.D of each set (which is not required ,But I calculated out of curiosity ) are:
a) 31.6
b) 15.8
c) 7.9

why are you subtracting each value of mean from 100?

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Tue Aug 01, 2017 9:02 pm
neha shekhawat wrote:
Hey Brent,
I am confused with the language of this question ( the absolute increase in their Standard Deviation, from largest to smallest? )
Is this question asking to arrange the S.D of all set in descending order?
I totally understand the concept of S.D, and looking at the given set and their spread I can easily see that first set has largest S.D and last set has the least S.D.
So if this question is asking about arranging the S.D in descending order then it would have been a,b,c.
But this is not the answer.
what is absolute increase in this case?
As when we calculate S.D of each set (which is not required ,But I calculated out of curiosity ) are:
a) 31.6
b) 15.8
c) 7.9

why are you subtracting each value of mean from 100?
Hi Neha,

"Is this question asking to arrange the S.D of all set in descending order?" is incorrect. The question does not ask this.

This question asks to arrange the ABSOLUTE INCREASE IN THE VALUES OF S.D of all set in descending order?

We need not be bothered about the values of the SDs of the three sets.

Say, currently the SDs of Sets A, B and C are a, b, and c, respectively. We need not know which value among a, b, and c is the largest and which is rhe smallest.

We are concerned with what happens when a new entrant '100,' is included in each set.

Say after the inclusion of '100,' the new SDs of three sets A, B, and C are (a + a'), (b + b'), and (c + c'), respectively; where a', b' and c' are the absolute increase in respective SD values.

The question asks us to arrange the values of a', b' and c' in descending order.

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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neha shekhawat Junior | Next Rank: 30 Posts
Joined
20 Jan 2017
Posted:
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Wed Aug 02, 2017 9:35 am
Thanks jay
I just realized that I missed the sentence (If number 100 is included in each of these sets) while reading the question.I straight away jumped on the sets.I have to pay more attention while reading such questions now.

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Matt@VeritasPrep GMAT Instructor
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Sun Aug 06, 2017 11:06 pm
neha shekhawat wrote:
Thanks jay
I just realized that I missed the sentence (If number 100 is included in each of these sets) while reading the question.I straight away jumped on the sets.I have to pay more attention while reading such questions now.
This is such a great lesson to learn from this problem. On the GMAT, of all places, is the devil IS in the details: subtle misreadings are deadly, and many of the questions are written to ENCOURAGE such misreadings!

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

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