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# A certain list has an average of 6 and a standard deviation

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A certain list has an average of 6 and a standard deviation [#permalink]

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18 Jul 2010, 12:33
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A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?

A. (-6;0)
B. (0;0)
C. (0;6)
D. (0;12)
E. (6;6)
[Reveal] Spoiler: OA
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18 Jul 2010, 13:09
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Raffy wrote:
A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?

a. (-6;0)
b. (0;0)
c. (0;6)
d. (0;12)
e. (6;6)

OA Later

"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."

So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.

According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.

Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.

For more on this issue please check Standard Deviation chapter of Math Book (link in my signature) and the following two topics for practice:
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18 Jul 2010, 22:39
thanks Bunuel, but is there any mathematical method also to calculate the same??
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27 Jul 2010, 14:45
Bunuel, you are a genius. Amazing explanation.
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28 Jul 2010, 01:23
Thank you Bunuel, I just add 1 following remark.
E is only correct if we take into account that d is positive. In case of d=0, the SD remains the same.
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24 Aug 2010, 17:29
How do answer choices C and E differ?

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6
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11 Jul 2012, 00:40
uzzy12 wrote:
How do answer choices C and E differ?

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6

Option E offers two numbers equal to the mean while other options (including C) offer number(s) different from the mean. Adding two numbers which are closest to the mean (option E in our case ) will shrink the set most, thus decreasing SD by the greatest amount.

Complete solution: a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html#p751013
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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11 Jul 2012, 09:49
+1 E

This is a conceptual question. If you add more data to the average, more data will be closer to the average. Hence, the standard deviation is lower.
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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11 Jul 2012, 22:14
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metallicafan wrote:
+1 E

This is a conceptual question. If you add more data to the average, more data will be closer to the average. Hence, the standard deviation is lower.

Yes, you are right. For a detailed discussion of this concept, check out these posts:

http://www.veritasprep.com/blog/2012/06 ... deviation/

http://www.veritasprep.com/blog/2012/06 ... n-part-ii/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 29 Nov 2012 Posts: 898 Followers: 14 Kudos [?]: 1083 [0], given: 543 Re: A certain list has an average of 6 and a standard deviation [#permalink] ### Show Tags 23 Jun 2013, 22:15 Tricky question! Is there an alternative solution? _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7182 Location: Pune, India Followers: 2164 Kudos [?]: 14009 [0], given: 222 Re: A certain list has an average of 6 and a standard deviation [#permalink] ### Show Tags 23 Jun 2013, 22:35 fozzzy wrote: Tricky question! Is there an alternative solution? This is a conceptual question. There is no so-called process that you can follow. You need to understand how SD is related to the average and the number of terms (through the SD formula). Once you do, you solve it by just looking at the options. Check out the links given above. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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24 Dec 2014, 12:10
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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17 May 2015, 16:51
Could someone explain what the question means by "must result in a list of 102 data" - that threw me off and I ended up completely ignoring that piece of information and was still able to get the question right but found it to be confusing.
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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17 May 2015, 19:05
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healthjunkie wrote:
Could someone explain what the question means by "must result in a list of 102 data" - that threw me off and I ended up completely ignoring that piece of information and was still able to get the question right but found it to be confusing.

It just means that with the addition of the two numbers, there will be 102 numbers in the list. So originally the list had 100 data points. In fact, the same question given here clarifies this: a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html#p769038
Since the question is conceptual, it doesn't matter much what the exact number of numbers are. It is just given to clarify that only 2 numbers were added and all others were retained.
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

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19 Jun 2016, 02:01
Hello from the GMAT Club BumpBot!

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Re: A certain list has an average of 6 and a standard deviation   [#permalink] 19 Jun 2016, 02:01
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