Which of the following pairs of numbers, when added to the set above, : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 06:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Which of the following pairs of numbers, when added to the set above,

Author Message
TAGS:

### Hide Tags

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 202 [1] , given: 16

Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

18 Oct 2012, 02:39
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:51) correct 52% (00:47) wrong based on 163 sessions

### HideShow timer Statistics

(9,12,15,18,21)

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

[Reveal] Spoiler:
Hi Bunnel,

This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning

I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1

I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

Regards
Srinath
[Reveal] Spoiler: OA

_________________

Intern
Joined: 18 Oct 2012
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 10

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

18 Oct 2012, 07:06
mydreammba wrote:
Hi Bunnel,

This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning

I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1

I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

Regards
Srinath

Mean of the above set would be = 15

so if the number added are closer to the mean then SD will decrease and vice-versa.
=> 14,16 will lower SD and other two would increase as copared to 14,16, but i think 15,100 would increase SD to the most, so i got confused as in which set to should be take as base to compare.

Thanks
Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 202 [0], given: 16

Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

05 Dec 2012, 19:35
2
This post was
BOOKMARKED
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

[Reveal] Spoiler:
i Mikemcgarry,

This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning

I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1

I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

Regards
Srinath

_________________

Manager
Joined: 26 Jul 2011
Posts: 126
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 106 [0], given: 15

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

06 Dec 2012, 02:39
My two cents on this....

more the values in the sets are away from the mean more is the standard deviation. I think as in the option 3 the number hundred will shoot up the standard deviation significantly and hence it would increase the standard deviation...Now we can see that the average of the set is 15 and option 1 and option 2 both has an average of 15 so both of them should not affect the SD...hence the answer should be the 3) 15, 100

Mike am I correct ??
Intern
Joined: 23 Nov 2012
Posts: 35
Location: France
Concentration: Finance, Economics
Schools: Said (D)
GMAT 1: 710 Q49 V38
WE: Sales (Investment Banking)
Followers: 0

Kudos [?]: 13 [0], given: 19

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

06 Dec 2012, 05:15
Think like that:

is the average total deviation of the two numbers to the mean of the set higher than the mean deviation of the numbers in the set?

or just take the mean of the lower half and the upper half of the set. if a number is outside this interval it will increase sd otherwise decrease
_________________

Hodor?

Kudo!

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 3639
Followers: 1249

Kudos [?]: 5656 [1] , given: 60

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

06 Dec 2012, 14:37
1
KUDOS
Expert's post
mydreammba wrote:
This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?
1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning
I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1
I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

I am responding to a pm from mydreammba.

First of all, your reasoning as regards these three pairs of numbers is perfectly correct. Option #2 increases the SD, option #3 flamboyantly increases the SD, and option #1 decreases the SD.

Now, as far as generalizing --- what you are suggesting there is not correct.

Think about mean first. Suppose Set Q has a mean of 7. If I add a new number that's more than the mean, more than 7, adding it to the set will increase the mean of the set. If I add a number that's less than the mean, less than 7, adding it to the set will decrease the mean of the set.

Well, the Standard Deviation is a kind of mean, a kind of average. If you add a pair of numbers, equal and opposite distances from the mean, whose deviations from the mean is (in absolute values terms) more than the standard deviation of the set, then adding these numbers will increase the average among the deviations from the mean, that is to say, it will increase the SD of the set. If you add a pair of numbers, equal and opposite deviations from the mean, whose distance from the mean is less than the standard deviation of the set, then adding these numbers will decrease the average among the deviations from the mean, that is to say, it will decrease the SD of the set. If you add numbers that are not symmetrically distributed with respect to the mean, then that changes the mean itself, which means every single value has a new deviation from the mean, so all bets are off (the test will not ask you about this case, unless it's really obvious, as in Option #3).

In problems like this, no one actually expects you to calculate the SD. The GMAT will not expect you to do that. You are just be asked to estimate.

Now, when I look at the set {9,12,15,18,21}, it's symmetrically distributed. I know the mean is 15. The deviations from the mean are {-6, -3, 0, 3, 6} ----- none of them in this particular set has an absolute value greater than six, so the SD absolutely can't be greater than 6 --- in fact it has to be less than 6. (Any average over several values has to be lower than the largest value.) That's why six is a crucial number in this particular case.

In the set {30, 40, 50, 60, 70}, the mean is 50, and the largest deviations from the mean are +/-20, so the SD must be less than 20. Adding {47, 53} would definitely decrease the SC. Adding {30, 70) would definitely increase the SD. Adding {30, 500) would also increase the SD.

Does all this make sense?

Mike
_________________

Mike McGarry
Magoosh Test Prep

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 202 [0], given: 16

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

08 Dec 2012, 22:29
mikemcgarry wrote:
mydreammba wrote:
This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?
1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning
I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1
I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

I am responding to a pm from mydreammba.

First of all, your reasoning as regards these three pairs of numbers is perfectly correct. Option #2 increases the SD, option #3 flamboyantly increases the SD, and option #1 decreases the SD.

Now, as far as generalizing --- what you are suggesting there is not correct.

Think about mean first. Suppose Set Q has a mean of 7. If I add a new number that's more than the mean, more than 7, adding it to the set will increase the mean of the set. If I add a number that's less than the mean, less than 7, adding it to the set will decrease the mean of the set.

Well, the Standard Deviation is a kind of mean, a kind of average. If you add a pair of numbers, equal and opposite distances from the mean, whose deviations from the mean is (in absolute values terms) more than the standard deviation of the set, then adding these numbers will increase the average among the deviations from the mean, that is to say, it will increase the SD of the set. If you add a pair of numbers, equal and opposite deviations from the mean, whose distance from the mean is less than the standard deviation of the set, then adding these numbers will decrease the average among the deviations from the mean, that is to say, it will decrease the SD of the set. If you add numbers that are not symmetrically distributed with respect to the mean, then that changes the mean itself, which means every single value has a new deviation from the mean, so all bets are off (the test will not ask you about this case, unless it's really obvious, as in Option #3).

In problems like this, no one actually expects you to calculate the SD. The GMAT will not expect you to do that. You are just be asked to estimate.

Now, when I look at the set {9,12,15,18,21}, it's symmetrically distributed. I know the mean is 15. The deviations from the mean are {-6, -3, 0, 3, 6} ----- none of them in this particular set has an absolute value greater than six, so the SD absolutely can't be greater than 6 --- in fact it has to be less than 6. (Any average over several values has to be lower than the largest value.) That's why six is a crucial number in this particular case.

In the set {30, 40, 50, 60, 70}, the mean is 50, and the largest deviations from the mean are +/-20, so the SD must be less than 20. Adding {47, 53} would definitely decrease the SC. Adding {30, 70) would definitely increase the SD. Adding {30, 500) would also increase the SD.

Does all this make sense?

Mike

Thanks Mike for a wonderful reply, now i get it
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6858

Kudos [?]: 90078 [0], given: 10413

Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 01:26
Expert's post
4
This post was
BOOKMARKED
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.
_________________
Moderator
Joined: 01 Sep 2010
Posts: 3033
Followers: 768

Kudos [?]: 6343 [1] , given: 991

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 02:43
1
KUDOS
1) The SD decreases

2) adding two equal terma at the edges of the distribution the SD increases

3) adding 100 at the end the SD increase

_________________
Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 20 [0], given: 113

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 07:22
I think all three increase the Stand deviation.

I went the traditional method with a bit of guessing. Please let me know if correct.

Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

_________________

Kudos to you, for helping me with some KUDOS.

Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 20 [0], given: 113

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 07:28
I think Carcass is right. My apologies.

Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

_________________

Kudos to you, for helping me with some KUDOS.

VP
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1342 [2] , given: 42

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 07:46
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

CONCEPT:Standard Deviation represents Average Deviation of the terms from the mean of the set

Rule 1: If the new terms included in the set are at a Higher distance from mean than the Standard Deviation will INCREASE
Rule 2: If the new terms included in the set are at a Lower distance from mean than the Standard Deviation will DECREASE

Set - {9, 12, 15, 18, 21} i.e. Mean = 15 (Middle Term as all terms are equally separated) and Deviation between consecutive terms = 3

I - New Set Becomes {9, 12, 14, 15, 16, 18, 21} i.e. New Terms (14,16) are closer to the Mean of the set Hence Standard Deviation will DECREASE

II - New Set Becomes {9, 9, 12, 15, 18, 21} i.e. New Terms (9,21) are at MORE Distance (greater than 3) from the Mean of the set Hence Standard Deviation will INCREASE

III - New Set Becomes {9, 12, 15, 18, 21, 51, 100} i.e. New Terms (51,100) are at FAR MORE Distance from the Mean of the set Hence Standard Deviation will INCREASE

[Reveal] Spoiler:
D

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 20 [0], given: 113

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 07:59
Hi GMATInsight,

Please could you help me with this question...as I am a bit weak in stats.

Rule 1: If the new terms included in the set are at a Higher distance from mean than the Standard Deviation will INCREASE

I want to know do we need to calculate the mean again after adding the new variables. I ask this question because you mentioned 'New Terms (9,21) are at MORE Distance (greater than 3)' , which are actually 6 units away from the mean.

GMATinsight wrote:
Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

CONCEPT:Standard Deviation represents Average Deviation of the terms from the mean of the set

Rule 1: If the new terms included in the set are at a Higher distance from mean than the Standard Deviation will INCREASE
Rule 2: If the new terms included in the set are at a Lower distance from mean than the Standard Deviation will DECREASE

Set - {9, 12, 15, 18, 21} i.e. Mean = 15 (Middle Term as all terms are equally separated) and Deviation between consecutive terms = 3

I - New Set Becomes {9, 12, 14, 15, 16, 18, 21} i.e. New Terms (14,16) are closer to the Mean of the set Hence Standard Deviation will DECREASE

II - New Set Becomes {9, 9, 12, 15, 18, 21} i.e. New Terms (9,21) are at MORE Distance (greater than 3) from the Mean of the set Hence Standard Deviation will INCREASE

III - New Set Becomes {9, 12, 15, 18, 21, 51, 100} i.e. New Terms (51,100) are at FAR MORE Distance from the Mean of the set Hence Standard Deviation will INCREASE

[Reveal] Spoiler:
D

_________________

Kudos to you, for helping me with some KUDOS.

VP
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1342 [0], given: 42

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 08:08
shriramvelamuri wrote:
Hi GMATInsight,

Please could you help me with this question...as I am a bit weak in stats.

Rule 1: If the new terms included in the set are at a Higher distance from mean than the Standard Deviation will INCREASE

I want to know do we need to calculate the mean again after adding the new variables. I ask this question because you mentioned 'New Terms (9,21) are at MORE Distance (greater than 3)' , which are actually 6 units away from the mean.

We don't have to calculate the New mean but look at the new set from the perspective of Mean of Old set only. The fact to observe is

Old set had consecutive terms at a gap of 3

The new terms 9 and 21, are at a gap higher than 3 from the previous mean (gap between 9 and 15=6 and similarly gap between 15 and 21 = 6), then the average deviation will automatically increase thereby increasing the standard deviation.

I hope it clears your doubt!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Verbal Forum Moderator
Joined: 29 Apr 2015
Posts: 899
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Followers: 49

Kudos [?]: 1167 [0], given: 302

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

23 Jun 2015, 11:46
Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

The set is evenly spaced with an average and median of 15. To increase the standard deviation of the set, we need to have numbers deviating as much as possible from the mean (15).

I. 14, 16 > they actually decrease the SD, being very close to the mean (i.e. having a smaller diffrence to the mean than 3)
II. 9, 21 > Clearly increase SD because 9 and 21 are farther away from 15
III. 15, 100 > Clearly increases SD with 100

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Manager
Joined: 01 Jan 2015
Posts: 56
Followers: 0

Kudos [?]: 2 [1] , given: 7

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

28 Jun 2015, 09:08
1
KUDOS
SD = deviation from the mean!
Added values closer to the mean/=mean = SD decreases
Added values if far away from the mean = SD Increases
if the set has same/equal values and you add more same values to the set = SD = 0
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6858

Kudos [?]: 90078 [0], given: 10413

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

29 Jun 2015, 05:30
Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Fortunately, you do not need to perform any calculations to answer this question. The mean of the set is 15. Take a look at each Roman Numeral:

I. The numbers 14 and 16 are both very close to the mean (15). Additionally, they are closer to the mean than four of the numbers in the set, and will reduce the spread around the mean. This pair of numbers will reduce the standard deviation of the set.

II. The numbers 9 and 21 are relatively far away from the mean (15). Adding them to the list will increase the spread of the set and increase the standard deviation.

III. While adding the number 15 to the set would actually decrease the standard deviation (because it is the same as the mean of the set), the number 100 is so far away from the mean that it will greatly increase the standard deviation of the set. This pair of numbers will increase the standard deviation.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6858

Kudos [?]: 90078 [0], given: 10413

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

29 Jun 2015, 05:31
Bunuel wrote:
Bunuel wrote:
{9, 12, 15, 18, 21}
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 16
II. 9, 21
III. 15, 100

(A) II only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Fortunately, you do not need to perform any calculations to answer this question. The mean of the set is 15. Take a look at each Roman Numeral:

I. The numbers 14 and 16 are both very close to the mean (15). Additionally, they are closer to the mean than four of the numbers in the set, and will reduce the spread around the mean. This pair of numbers will reduce the standard deviation of the set.

II. The numbers 9 and 21 are relatively far away from the mean (15). Adding them to the list will increase the spread of the set and increase the standard deviation.

III. While adding the number 15 to the set would actually decrease the standard deviation (because it is the same as the mean of the set), the number 100 is so far away from the mean that it will greatly increase the standard deviation of the set. This pair of numbers will increase the standard deviation.

Check other Standard Deviation Questions in our Special Questions Directory.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12903
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

11 Dec 2015, 01:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 09 Dec 2014
Posts: 47
GMAT 1: 600 Q42 V32
GMAT 2: 710 Q48 V38
GPA: 3.7
Followers: 1

Kudos [?]: 18 [0], given: 830

Re: Which of the following pairs of numbers, when added to the set above, [#permalink]

### Show Tags

30 Dec 2015, 01:10
mydreammba wrote:
Hi Bunnel,

This is a problem from Manhattan 13th Edition

consider Set {9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

1. 14, 16
2. 9, 21
3. 15, 100

Here is my reasoning

I know that with Options 2 & Option 3 the SD will increase as we are adding numbers whose difference between Mean the corresponding new adding number is maximum i.e the difference is >= the max difference between any two numbers prior to the adding of the two new numbers.

Now with Option 1

I know that the numbers are closer to mean so SD will decrease, but here can i generalize always that for SD to increase the two new added numbers must be such that the difference between the two new added numbers and the mean must always be >=6 or it is enough if the difference between one new added number (among the two numbers) and the mean is >=6 ?

I think i am making things complex, but don't know somehow got confused....

Regards
Srinath

Option 3: 15 and 100 will increase the SD the most. Option 2 would also increase the SD but not as much as Option 3 would.
Re: Which of the following pairs of numbers, when added to the set above,   [#permalink] 30 Dec 2015, 01:10

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
5 For the sets of numbers above, which of the following is true? 8 16 Jun 2015, 02:42
4 In which of the following pairs are the two numbers reciprocals of one 5 11 Jan 2015, 11:29
7 In which of the following pairs are the two numbers reciproc 8 26 Dec 2013, 07:56
5 The numbers in which of the following pairs do NOT have 5 28 Apr 2012, 20:43
6 Which of the following series of numbers, if added to the 6 26 Jan 2012, 11:35
Display posts from previous: Sort by