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# The set Q has a mean of 31 and a standard deviation of 4. Which of the

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Manager
Joined: 31 May 2018
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The set Q has a mean of 31 and a standard deviation of 4. Which of the  [#permalink]

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02 Aug 2019, 08:08
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The set Q has a mean of 31 and a standard deviation of 4. Which of the following pairs of numbers will decrease the standard deviation the most if they are added to the set?

A) {26, 36}

B) {27, 34}

C) {28, 42}

D) {30, 32}

E) {34, 34}
Intern
Joined: 12 Apr 2018
Posts: 14
Re: The set Q has a mean of 31 and a standard deviation of 4. Which of the  [#permalink]

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02 Aug 2019, 08:23
I got this wrong. Can anyone please post some resource for understanding this topic.
Regards,

Posted from my mobile device
Senior Manager
Joined: 20 Mar 2018
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Location: Ghana
Concentration: Finance, Real Estate
The set Q has a mean of 31 and a standard deviation of 4. Which of the  [#permalink]

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02 Aug 2019, 09:13
The set Q has a mean of 31 and a standard deviation of 4. Which of the following pairs of numbers will decrease the standard deviation the most if they are added to the set?

This simple : We are given Mean(m)=31 ,deviation(d)=4
Now list numbers we can derive is
....m-2d,m-d,m,m+d,m+2d...etc
So ...23,27,31,35...
Now, any number close to the mean when added decreases the variation as much as possible ,the vice versa is also true

A) {26, 36}
This will increase the deviation as 26 and 36 is very far from mean (31)

B) {27, 34}
Same as in A

C) {28, 42}
Same as in A

D) {30, 32}
You notice that 32,30 are close to mean ,Hence this decreases the variation (correct)

E) {34, 34}
Nope increases deviation

Hence D

For in-depth understanding of statistics visit https://gmatclub.com/forum/statistics-m ... l#p1563176
Hope it helps

sanjayparihar16 wrote:
I got this wrong. Can anyone please post some resource for understanding this topic.
Regards,

Posted from my mobile device
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Re: The set Q has a mean of 31 and a standard deviation of 4. Which of the  [#permalink]

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04 Aug 2019, 11:38
1
shridhar786 wrote:
The set Q has a mean of 31 and a standard deviation of 4. Which of the following pairs of numbers will decrease the standard deviation the most if they are added to the set?

A) {26, 36}

B) {27, 34}

C) {28, 42}

D) {30, 32}

E) {34, 34}

Numbers added to a set that will decrease the standard deviation of the set the most are those that are closest to the mean of the set. Since the mean of set Q is 31, data points of 30 and 32 will decrease the standard deviation of set Q the most since they are closer to 31 than the data points given in other choices.

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Re: The set Q has a mean of 31 and a standard deviation of 4. Which of the   [#permalink] 04 Aug 2019, 11:38
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