It is currently 12 Dec 2017, 14:06

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Which of the following distribution of numbers has the greatest standa

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [0], given: 12691

Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 10:40
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (00:53) correct 30% (00:47) wrong based on 122 sessions

HideShow timer Statistics

Which of the following distribution of numbers has the greatest standard deviation?

(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [0], given: 12691

SC Moderator
User avatar
P
Joined: 13 Apr 2015
Posts: 1507

Kudos [?]: 1226 [0], given: 895

Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
GMAT ToolKit User Premium Member CAT Tests
Re: Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 11:12
Bunuel wrote:
Which of the following distribution of numbers has the greatest standard deviation?

(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}


Hi Bunuel,

Both A and D can be the answer for the above question.

Kudos [?]: 1226 [0], given: 895

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135384 [1], given: 12691

Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 11:25
1
This post received
KUDOS
Expert's post
Vyshak wrote:
Bunuel wrote:
Which of the following distribution of numbers has the greatest standard deviation?

(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}


Hi Bunuel,

Both A and D can be the answer for the above question.


Those two sets have different standard deviations.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135384 [1], given: 12691

1 KUDOS received
Manager
Manager
User avatar
B
Joined: 16 Mar 2016
Posts: 134

Kudos [?]: 52 [1], given: 0

Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
GMAT ToolKit User
Re: Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 12:09
1
This post received
KUDOS
A => sd =\sqrt{14/3}
B => sd =\sqrt{10/4}
C => sd =\sqrt{8/3}
D => sd =\sqrt{14/4}
E => sd =\sqrt{11/3}

So the biggest is A.

Kudos [?]: 52 [1], given: 0

Intern
Intern
avatar
Joined: 21 Oct 2015
Posts: 46

Kudos [?]: 7 [0], given: 115

GMAT 1: 620 Q47 V28
GMAT ToolKit User
Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 20:20
Let me try this one:

First, we find the mean for every set. After you find the mean, look for distance between mean and outliers (numbers on boundary of distribution - MAX |m-n|, where m is mean and n is any number in set). You can ignore choices B, C, and E based on that understanding. Remaining two choices have same distance = 3.

Next, we look at density of distribution in remaining two options. More numbers between mean and outlier, more denser the set become. More denser the set become, less deviation it provides. Based on that understanding, D should have lesser standard deviation between remaining two.

Answer - A.

Comments welcome. Its been ages since I last tried SD.

Posted from my mobile device

Kudos [?]: 7 [0], given: 115

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7791

Kudos [?]: 18108 [2], given: 236

Location: Pune, India
Re: Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 18 May 2016, 21:27
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
Which of the following distribution of numbers has the greatest standard deviation?

(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}



For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2
For answer choice C, the mean = 5 and the deviations are 2, 0, 2
For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2
For answer choice E, the mean = 2 and the deviations are 2, 0, 2

We don’t need to worry about the arithmetic means (they just help us calculate the deviation of each element from the mean); our focus should be on the deviations. The SD formula squares the individual deviations and then adds them, then the sum is divided by the number of elements and finally, we find the square root of the whole term. So if a deviation is greater, its square will be even greater and that will increase the SD.

If the deviation increases and the number of elements increases, too, then we cannot be sure what the final effect will be – an increased deviation increases the SD but an increase in the number of elements increases the denominator and hence, actually decreases the SD. The overall effect as to whether the SD increases or decreases will vary from case to case.

First, we should note that answers C and E have identical deviations and numbers of elements, hence, their SDs will be identical. This means the answer is certainly not C or E, since Problem Solving questions have a single correct answer.

Let’s move on to the other three options:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2
For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2

Comparing answer choices A and D, we see that they both have the same deviations, but D has more elements. This means its denominator will be greater, and therefore, the SD of answer D is smaller than the SD of answer A. This leaves us with options A and B:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2

Now notice that although two deviations of answers A and B are the same, answer choice A has a higher deviation of 3 but fewer elements than answer choice B. This means the SD of A will be higher than the SD of B, so the SD of A will be the highest. Hence, our answer must be A.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18108 [2], given: 236

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 903

Kudos [?]: 454 [0], given: 69

Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 19 May 2016, 19:38
IMHO 'A' should be the answer.

Lets look at average and Std deviation respectively in every choice

A) 0 / 5
B) 0/ 4
C) 3/4
D) 2/5
E) 2/4

Clearly 'A' has the greatest SD :)
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Kudos [?]: 454 [0], given: 69

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14897

Kudos [?]: 287 [0], given: 0

Premium Member
Re: Which of the following distribution of numbers has the greatest standa [#permalink]

Show Tags

New post 26 Oct 2017, 03:47
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Re: Which of the following distribution of numbers has the greatest standa   [#permalink] 26 Oct 2017, 03:47
Display posts from previous: Sort by

Which of the following distribution of numbers has the greatest standa

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.