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If the positive number d is the standard deviation of n, k and p then

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If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post Updated on: 03 May 2017, 22:23
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A
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D
E

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Question Stats:

81% (00:36) correct 19% (00:36) wrong based on 187 sessions

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If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1 and p+1 is

(A) d+3
(B) d+1
(C) 6d
(D) 3d
(E) d

Originally posted by mun23 on 19 Feb 2013, 06:59.
Last edited by Bunuel on 03 May 2017, 22:23, edited 2 times in total.
Edited the question.
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Re: If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post 19 Feb 2013, 09:09
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mun23 wrote:
If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1 and p+1 is

(A) d+3
(B) d+1
(C) 6d
(D) 3d
(E) d


GyanOne is absolutely right about the answer, it is indeed E. I've often heard students say that standard deviation is their least favorite statistic. I, however, think that it should be the opposite. Calculating a square root may seem tedious to some, but the GMAT never asks you to do the actual calculations, so the questions always revolve around the concept. In this case, whether the numbers n, k and p are all increased by 1 or 100, or even 5,000,000, the answer remains the same. The only time the standard deviation is going to increase or decrease is if the numbers are multiplied (or divided, which is really just multiplication by 1/number) by some constant.

A standard deviation question is an opportunity to get easy points because the concept being tested will never be that hard. The important notions are that moving the numbers by a constant changes nothing, multiplying amplifies everything (as you would by pinching an iphone screen) and that sets with the same numbers have standard deviations of 0 (ex: 5,5,5,5).

Quick refresher to calculate standard deviation:
1) Take the average of all numbers.
2) Subtract the average from each element of the set
3) Square this difference (they're all positive now)
4) Add up all these numbers and divide by the number of elements
5) Take the square root of this number. (note: the square is the variance, not tested on the GMAT)

Again, you don't ever have to do this on the GMAT, but the concep can help unlock quick answers to standard deviation questions.
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Re: If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post 19 Feb 2013, 08:42
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If all the observations of a data set change by the same amount, the standard deviation remains the same.

The standard deviation of the new set is also therefore d.

E is the answer.
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Re: If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post 19 Feb 2013, 09:42
mun23 wrote:
If the positive number d is the standard deviation of n, k and p then the standard deviation of n+1, k+1 and p+1 is

(A) d+3
(B) d+1
(C) 6d
(D) 3d
(E) d

Maybe if the theory is not known, one of methods might be to plugin numbers. Assume n,k,p as 1,2,3. Initially, S.D =\(\sqrt{\frac{(1-2)^2+0^2+(3-2)^2}{3}}\) = \(\sqrt{\frac{2}{3}}\). Similarly, S.D for 2,3,4 will be \(\sqrt{\frac{(2-3)^2+0^2+(4-3)^2}{3}}\) = \(\sqrt{\frac{2}{3}}\)

Thus its the same.

E.
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Re: If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post 22 Feb 2013, 09:00
vinaymimani wrote:
Maybe if the theory is not known, one of methods might be to plugin numbers. Assume n,k,p as 1,2,3. Initially, S.D =\(\sqrt{\frac{(1-2)^2+0^2+(3-2)^2}{3}}\) = \(\sqrt{\frac{2}{3}}\). Similarly, S.D for 2,3,4 will be \(\sqrt{\frac{(2-3)^2+0^2+(4-3)^2}{3}}\) = \(\sqrt{\frac{2}{3}}\)

Thus its the same.

E.


I'm a big fan of plugging in a few numbers if the theory is a little vague. Instead of racking your brain trying to remember some obscure rule (like odd x odd = even/odd?), just try with numbers and you'll see the answer quickly (3 x 5=15, so the product of odd x odd must be odd).

Always a good suggestion to keep in mind that we can proceed this way, thanks Vinaymimani!
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If the positive number d is the standard deviation of n, k, and  [#permalink]

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New post 03 May 2017, 21:23
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peterpark wrote:
If the positive number d is the standard deviation of n, k, and p, then the standard deviation of n + 1, k + 1, and p + 1 is

A) d + 3

B) d + 1

C) 6d

D) 3d

E) d


Standard deviation depends on the relative placement of numbers with respect to each other only.

So standard deviation in these two cases is the same :

--------n---k-----p-----------
----------n---k-----p---------

Hence the standard deviation of the new set will be d only.

Answer (E)

For more on SD, check here: https://www.veritasprep.com/blog/2012/0 ... deviation/
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If the positive number d is the standard deviation of n, k and p then  [#permalink]

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New post 20 Aug 2017, 09:03
Though two great instructors from Veritas Prep have already commented on this, I will take the liberty to Quote the "Map Strategy" from Veritas Prep Book to help remember how SD behaves when a constant is added/subtracted/Multiplied/divided to a set. I hope you find it helpful.

Map Strategy for Standard Deviation (Courtesy - Veritas Prep Statistics and combinatorics book)

  • Adding or subtracting a constant from each element in the set has no effect on the standard deviation. Shifting a map does not change the distances.
  • Multiplying each term of a set by a number with an absolute value greater than 1 increases the standard deviation, while multiplying by a number with an absolute value less than 1 decreases the standard deviation. Increasing the scale of the map increases distances, while reducing the scale shrinks them.
  • Dividing each element in a set by a number with an absolute value greater than 1 decreases the standard deviation, while dividing by a number with an absolute value less than 1 increases the standard deviation. Increasing the scale of the map increases distances, while reducing the scale shrinks them.
  • Changing the sign of all elements in the set or multiplying by -1 has no effect on the standard deviation.

Applying the "Map Strategy" to this question we see that a constant is added to every element of the set. Hence, the SD will remain unchanged. The Required answer is E.
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If the positive number d is the standard deviation of n, k and p then   [#permalink] 20 Aug 2017, 09:03
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