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# Math: Standard Deviation

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Board of Directors
Joined: 17 Jul 2014
Posts: 2420
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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24 Dec 2015, 09:12
I have a question related to SD.

if a number is exactly the mean, is it considered within 1 SD from the mean?
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Joined: 02 Sep 2009
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24 Dec 2015, 10:41
mvictor wrote:
I have a question related to SD.

if a number is exactly the mean, is it considered within 1 SD from the mean?

_______________________
Yes.
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Joined: 20 Mar 2014
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Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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24 Dec 2015, 16:51
mvictor wrote:
I have a question related to SD.

if a number is exactly the mean, is it considered within 1 SD from the mean?

Yes because technically en element = mean of the set will be at exactly 0 Standard deviations from the mean and as such it will be within 1 or 2 or 3 etc SDs.
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Joined: 18 Jul 2016
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23 Aug 2016, 17:25
Quote:
Example #3
Q: Standard deviation of set {23,31,76,45,16,55,54,36}{23,31,76,45,16,55,54,36} is 18.3. How many elements are 1 standard deviation above the mean?
Solution: Let's find mean: \m=23+31+76+45+16+55+54+368=42\m=23+31+76+45+16+55+54+368=42
Now, we need to count all numbers greater than 42+18.3=60.3. It is one number - 76. The answer is 1.

Kindly correct me if I am wrong
I think elements that are 1 standard deviation (d) above the mean(m) = elements within 'm' and 'm+d'
so shouldn't it be elements within 42 and 60.3?
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Joined: 28 Nov 2014
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06 Sep 2016, 03:07
1
I have a question regarding standard deviation. I am unsure about how to solve standard deviation's comparing sets questions. For example: If I am given a set and asked as to what of the following options have the standard deviation closest to the one given in question. Questions such as

Which of the following options have the standard deviation closest to the standard deviation to set A = [10,15,20,25,30]

A [30,40,50,60,70]
B [5,15,25,35,45]
C [20, 35, 50, 65, 80]
D [ -20,-10,0,10,20]
E [24, 40, 56, 80,96]

How do I compare these options with the one given in the question?
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Joined: 17 May 2015
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25 Jun 2017, 05:12
keats wrote:
I have a question regarding standard deviation. I am unsure about how to solve standard deviation's comparing sets questions. For example: If I am given a set and asked as to what of the following options have the standard deviation closest to the one given in question. Questions such as

Which of the following options have the standard deviation closest to the standard deviation to set A = [10,15,20,25,30]

A [30,40,50,60,70]
B [5,15,25,35,45]
C [20, 35, 50, 65, 80]
D [ -20,-10,0,10,20]
E [24, 40, 56, 80,96]

How do I compare these options with the one given in the question?

Hi keats,
In the set A gap between consecutive terms is 5. Now, check for all the options.

(A) Gap 10
(B) Gap 10
(C) Gap 15
(D) Gap 10
(E) Gap 16,16,24, and 16.

There is no unique answer to this question. Option (A), (B) and (D) will have closest Standard Deviation (SD) to the Set A.

You don't need to compute the SD for all the options.

Some more information we can deduce from the above-given data set without computing SD.

=> Option (A), (B), and (D) will have the same SD. Because SD doesn't change with addition or subtraction of a constant number.

=> Option (E) will have highest SD among all.

Hope this helps.
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Joined: 06 Jul 2017
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17 Sep 2017, 02:36
Shouldn't the divisor be (N-1) for the variance and the standard variation

--> variance=∑(xi−xav)^2/(N-1)
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Joined: 02 Sep 2009
Posts: 65808

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17 Sep 2017, 02:42
1
oli29 wrote:
Shouldn't the divisor be (N-1) for the variance and the standard variation

--> variance=∑(xi−xav)^2/(N-1)

Check this: https://gmatclub.com/forum/definition-o ... ml#p850040
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Joined: 27 Feb 2019
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21 Oct 2019, 20:45
walker wrote:
...or it means that Standard deviation of any 39 consecitive even integers will be same as they are equally distributed with respect to the avarge ?

Exactly. Let's look at simple example,

{4,6,8} and {1004,1006,1008} they have the same STD because all elements of second set are shifted by constant number 1000.

I think may be the question should be re-phrase to yes or no question( Can we find the SD? answer :YES, st 1 is enough to find the SD) , instead of what is the SD because I am sure knowing number of elements in the set i.e 39 is not enough to calculate the SD but it is enough to answer YES.
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07 Apr 2020, 06:26
Hello thank you for this post.Is this all we have to know about SD in all GMAT? Thank you for the reply.
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Re: Math: Standard Deviation   [#permalink] 07 Apr 2020, 06:26

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