A set consists of 20 different....

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A set consists of 20 different....

by Vincen » Mon Oct 02, 2017 9:57 am

A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

The OA is C.

I don't know how can I solve this PS question. I don't understand what is standard deviation. Experts could you explain this to me please?

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Source: Beat The GMAT — Problem Solving | Mon Oct 02, 2017 9:57 am

jbryant62: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Nov 23, 2016 4:04 pm; Thanked: 1 times

by jbryant62 » Mon Oct 02, 2017 12:59 pm

Vincen wrote:A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

The OA is C.

I don't know how can I solve this PS question. I don't understand what is standard deviation. Experts could you explain this to me please?

I am not an "expert" but standard deviation is just the dispersion of numbers or variance in regards to the mean. So for example, a set of 2,2,2 would have a standard deviation of 0, since there is no variance. The GMAT doesn't really test your knowledge of how to calculate SD, you just need to understand the principle.
As to the question, since you have a group of 20 random numbers, whose mean is 10 , the closer the numbers to the mean will reduce the standard deviation. In this problem, you are adding two numbers whose deviation is 0.

Hope that made sense. Maybe an expert can opine and explain it better.

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GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Mon Oct 02, 2017 1:27 pm

I think jbryant's explanation was great! We definitely do not need to calculate SD ever on the GMAT. In fact, I train my students to read "standard deviation" as "spread-out-ness." E.g. "which set has the greater standard deviation?" = "which set is more spread out overall?"

Imagine the set [5, 10, 15].
What would make it more spread out? --> adding terms that were further from the mean of 10: [0, 5, 10, 15, 20].
What would make it less spread out? --> adding terms that were closer to the mean: [5, 9, 10, 11, 15]

The thing that would be least spread out of all - the thing that would lower the standard deviation - would be the mean itself: 10.

Does that help?

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Quote

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Mon Oct 02, 2017 1:30 pm

Here are other examples for which we can think of standard deviation as "spread-out-ness":
https://www.beatthegmat.com/standard-dev ... tml#724642
https://www.beatthegmat.com/std-t63554.html#739837
https://www.beatthegmat.com/call-for-hel ... tml#545420
https://www.beatthegmat.com/standard-dev ... tml#680908

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: A set consists of 20 different....

by Scott@TargetTestPrep » Tue Jan 28, 2020 5:53 am

Vincen wrote: ↑
Mon Oct 02, 2017 9:57 am
A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

The OA is C.

I don't know how can I solve this PS question. I don't understand what is standard deviation. Experts could you explain this to me please?

The standard deviation is a measure of how far the data values of a set are located from the average. When new values that are equal to the average are added to the set, the standard deviation is decreased because these new values have no deviation from the average.

In the given data set, since the average is 10, when 10 and 10 are added to the set, the standard deviation will certainly decrease. The other pairs may or may not decrease the standard deviation.

Answer: C

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