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Manager  Joined: 06 Apr 2010
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What is SD of given set of numbers whose average is 5?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 66% (00:51) correct 34% (01:01) wrong based on 193 sessions

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What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 0 when value of each of the given number is increased by 7

Originally posted by udaymathapati on 31 Oct 2010, 04:26.
Last edited by Bunuel on 29 Mar 2017, 04:21, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: What is SD of given set of numbers whose average is 5?  [#permalink]

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udaymathapati wrote:
What is SD of given set of numbers whose average is 5?
1. None of the numbers are greater than this Average
2. The Standard deviation is 5 when value of each of the given number is increased by 7

Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

We need to know couple of important properties for this question:

If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

You can try it yourself:
SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set.

That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant.

Also: If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

That's because if a list contains all identical elements then there is no variation from the mean, hence SD=0.

BACK TO THE ORIGINAL QUESTION:

What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average --> if no number is more than the mean then no number is less than mean, which implies that this list contains all identical elements (or which is the same just one element), so SD=0. Sufficient.

(2) The Standard deviation is 0 when value of each of the given number is increased by 7 --> if we add or subtract a constant to each term in a set SD will not change, so SD=0. Sufficient.

For more on Standard Deviation check:
math-standard-deviation-87905.html

Hope it helps.
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Manager  Joined: 09 Jun 2010
Posts: 91
Re: What is SD of given set of numbers whose average is 5?  [#permalink]

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Something is wrong with this one. I read somewhere that in DS question both the options should give same result if both are sufficient.

From statement:1

Mean = 5 and none of the elements are greater than the mean => all the items in the set are identical therefore the SD = 0; all the items are 5.

Statement: 2

Adding a constant to all the items will not change the SD. Therefore the SD of the original set = 5

The answer is D by the way since both the statements give the SD.
Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: What is SD of given set of numbers whose average is 5?  [#permalink]

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soumanag wrote:
Something is wrong with this one. I read somewhere that in DS question both the options should give same result if both are sufficient.

From statement:1

Mean = 5 and none of the elements are greater than the mean => all the items in the set are identical therefore the SD = 0; all the items are 5.

Statement: 2

Adding a constant to all the items will not change the SD. Therefore the SD of the original set = 5

The answer is D by the way since both the statements give the SD.

You are right: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

There must be a typo in (2) and it should read "The Standard deviation is 0 when ..."
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Re: What is SD of given set of numbers whose average is 5?  [#permalink]

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udaymathapati wrote:
What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 5 when value of each of the given number is increased by 7

Hi Moderators,

Could you kindly edit statement (2):

It should read "The Standard deviation is 0 when ..."

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: What is SD of given set of numbers whose average is 5?  [#permalink]

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duahsolo wrote:
udaymathapati wrote:
What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 5 when value of each of the given number is increased by 7

Hi Moderators,

Could you kindly edit statement (2):

It should read "The Standard deviation is 0 when ..."

Thanks

Edited. Thank you.
_________________ Re: What is SD of given set of numbers whose average is 5?   [#permalink] 29 Mar 2017, 04:22
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