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Math: Standard Deviation

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Re: Math: Standard Deviation  [#permalink]

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New post 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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Re: Math: Standard Deviation  [#permalink]

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New post 24 Dec 2015, 10:41
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Re: Math: Standard Deviation  [#permalink]

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New post 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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Re: Math: Standard Deviation  [#permalink]

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New post 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?
Thanks in advance.:)
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Re: Math: Standard Deviation  [#permalink]

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New post 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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Re: Math: Standard Deviation  [#permalink]

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New post 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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Re: Math: Standard Deviation  [#permalink]

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New post 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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New post 17 Sep 2017, 02:42
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Re: Math: Standard Deviation  [#permalink]

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New post 19 Sep 2018, 09:10
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Re: Math: Standard Deviation &nbs [#permalink] 19 Sep 2018, 09:10

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