It is currently 25 Feb 2018, 19:41

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

Set X consists of 100 numbers. The average (arithmetic mean)

Author Message
TAGS:

Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

30 May 2010, 05:49
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

63% (00:42) correct 37% (00:51) wrong based on 435 sessions

HideShow timer Statistics

Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 24 Sep 2015, 02:52, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 27 Aug 2009
Posts: 45
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

30 May 2010, 06:22
4
KUDOS
Hussain15 wrote:
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

A. -100 & -100
B. -10 & -10
C. 0 & 0
D. 0 & 20
E. 10 & 10

Standard Deviation is deviation from the mean. If all the numbers in a set are equal to mean, then the standard deviation will be zero.
Therefore, in the given set with mean of 10, if we add 10 & 10, then the standard deviation will reduce. All other numbers will increase the standard deviation.

Please note that B is not the answer. Mean is +10 and, therefore, -10 is 20 points away from +10 (its not equal to the mean). Therefore, -10 will increase the standard deviation of the given set.
_________________

Salaries are low in recession. So, working for kudos now.

Manager
Joined: 04 Apr 2010
Posts: 88
Schools: UCLA Anderson
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

02 Jun 2010, 16:48
Clearly E, as the mean of the set is 10. Adding the mean as an extra value in the set will decrease the standard deviation.
_________________

Manager
Joined: 16 Mar 2010
Posts: 170
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 02:41
I have a doubt for this explaination.
The question says "will decrease the set’s standard deviation by the GREATEST amount" Now if SD is +ve then adding a negetive number will reduce the standard deviation correct?? and if SD is -ve then adding the positive number will reduce the standard deviation. the value of the added will depend on the number of data given.
Please correct me if i am wrong.
Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 05:04
I have another doubt:

If we will add 10 & 10 to set X, then the arithematic mean will not change i.e it will still be 10. Hence the standar deviation will not change & will remain the same. But our requirement is that SD will decrease in maximum.

What am I missing here?
_________________
Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 05:14
Hussain15 wrote:
I have another doubt:

If we will add 10 & 10 to set X, then the arithematic mean will not change i.e it will still be 10. Hence the standar deviation will not change & will remain the same. But our requirement is that SD will decrease in maximum.

What am I missing here?

I think the red portion in my statement above is not correct. SD will come down.
_________________
Director
Joined: 24 Aug 2007
Posts: 923
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 05:43
Yes, this part is incorrect.

There will be no change in the average if you add (10, 10), but the difference will be zero, when we calculate for SD. So, SD will be <4.6.

E is correct, which brings the miminum sum after subtracting and squaring the differences for SD calculations.

Hussain15 wrote:
Hussain15 wrote:
I have another doubt:

If we will add 10 & 10 to set X, then the arithematic mean will not change i.e it will still be 10. Hence the standar deviation will not change & will remain the same. But our requirement is that SD will decrease in maximum.

What am I missing here?

I think the red portion in my statement above is not correct. SD will come down.

_________________

Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 05:49
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
Hussain15 wrote:
Hussain15 wrote:
I have another doubt:

If we will add 10 & 10 to set X, then the arithematic mean will not change i.e it will still be 10. Hence the standar deviation will not change & will remain the same. But our requirement is that SD will decrease in maximum.

What am I missing here?

I think the red portion in my statement above is not correct. SD will come down.

"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 10 and 10 (actually these numbers equal to the mean) thus adding them will shrink the set most, thus decreasing SD by the greatest amount.

amitjash wrote:
I have a doubt for this explaination.
The question says "will decrease the set’s standard deviation by the GREATEST amount" Now if SD is +ve then adding a negetive number will reduce the standard deviation correct?? and if SD is -ve then adding the positive number will reduce the standard deviation. the value of the added will depend on the number of data given.
Please correct me if i am wrong.

SD is always $$\geq{0}$$. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

For more on this issue please check Standard Deviation chapter of Math Book (link in my signature) and the following two topics for practice:
_________________
Manager
Joined: 04 Apr 2010
Posts: 88
Schools: UCLA Anderson
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

04 Jun 2010, 09:48
1
KUDOS
You can prove it yourself with a couple quick calculations. Try calculating the SD for the set

{1,2,3}

and then calculate it for the set

{1,2,2,3}

Notice how it decreases.
_________________

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 309
Set X consists of 100 numbers. The average (arithmetic mean) [#permalink]

Show Tags

24 Oct 2010, 13:05
1
This post was
BOOKMARKED
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10
_________________

I'm the Dumbest of All !!

Math Expert
Joined: 02 Sep 2009
Posts: 43917

Show Tags

24 Oct 2010, 13:10
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
shrive555 wrote:
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10

"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 10 and 10 (actually these numbers equal to the mean) thus adding them will shrink the set most, thus decreasing SD by the greatest amount.

For more on this issue please check Standard Deviation chapter of Math Book (link in my signature) and the following two topics for practice:

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43917
Re: Set X consists of 100 numbers. The average (arithmetic mean) [#permalink]

Show Tags

08 Dec 2013, 23:33
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
gmatgambler wrote:
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

A)-100 and -100
B)-10 and -10
C)0 and 0
D)0 and 20
E)10 and 10

Merging similar topics. Please refer to the solutions above.

Theory on Statistics and Sets problems: math-standard-deviation-87905.html

All DS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=34
All PS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=55

Similar questions to practice:
a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html
a-certain-list-of-100-data-has-an-average-arithmetic-mean-87743.html
a-certain-list-of-200-test-scores-has-an-average-131448.html
new-ds-set-150653-60.html#p1211907

Hope this helps.
_________________
Intern
Joined: 29 May 2014
Posts: 17
Concentration: Finance, Strategy
GPA: 3.8
Re: Set X consists of 100 numbers. The average (arithmetic mean) [#permalink]

Show Tags

14 Jun 2014, 04:51
How I think about problems associated with means and standard deviations is with scattered data points. Since this question is regarding standard deviations (and how to reduce it), a quantity calculated to indicate the extent of deviation for the group -- the greater the deviation from the mean the greater the standard deviation. Therefore what data points will help to reduce deviation from the mean of set X [10]. If you add two points with the value of the mean their deviation will be 0, which is the smallest deviation you can add to the set of numbers.
Manager
Joined: 20 Apr 2014
Posts: 113
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set X [#permalink]

Show Tags

24 Sep 2015, 01:33
i reviewed math of Gmat club and found that 10,10 will not decrease the SD
Senior Manager
Joined: 17 Jun 2015
Posts: 258
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
Re: Set X consists of 100 numbers. The average (arithmetic mean) [#permalink]

Show Tags

25 Dec 2015, 12:01
HIgh SD = Wide distribution of data in the set
Low SD = Closely associated data in the set

The intention is to reduce the SD

That implies the newer entrants into the set need to near the mean

Option A would Increase the SD the most
Option E would not affect as much.

Hence E
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Non-Human User
Joined: 09 Sep 2013
Posts: 13746
Re: Set X consists of 100 numbers. The average (arithmetic mean) [#permalink]

Show Tags

01 Apr 2017, 13:53
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.
_________________
Re: Set X consists of 100 numbers. The average (arithmetic mean)   [#permalink] 01 Apr 2017, 13:53
Display posts from previous: Sort by