Author 
Message 
TAGS:

Hide Tags

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 960
Location: Singapore

E is a collection of four ODD integers and the greatest [#permalink]
Show Tags
25 Aug 2010, 07:41
5
This post received KUDOS
25
This post was BOOKMARKED
Question Stats:
44% (02:08) correct
56% (03:51) wrong based on 435 sessions
HideShow timer Statistics
E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Please press kudos if you like my post.



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: Hard  standard deviation [#permalink]
Show Tags
25 Aug 2010, 08:43
I know this question, I've posted it in my topic: psquestionsaboutstandarddeviation85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 05 Jul 2010
Posts: 3

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 01:10
hello. i would very appreciate if you can tell why in the end it became 4 instead of 3
"So SD of such set can take only 4 values." thanks in advance



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 01:25
anishok wrote: hello. i would very appreciate if you can tell why in the end it became 4 instead of 3
"So SD of such set can take only 4 values." thanks in advance Sets with distinct SD: 1. {1, 1, 1, 5}; 2. {1, 1, 3, 5}; 3. {1, 1, 5, 5}; 4. {1, 3, 3, 5};So 4 different values of SD. 5. SD of {1, 3, 5, 5} equals to SD of 2. {1, 1, 3, 5}; 6. SD of {1, 5, 5, 5} equals to SD of 1. {1, 1, 1, 5}. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 01:53
Very good but time consuming question. Bunuel do you think it is a Gmat Question.?
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 07:20
1
This post received KUDOS
2
This post was BOOKMARKED
gurpreetsingh wrote: Very good but time consuming question.
Bunuel do you think it is a Gmat Question.? I dont think this is a hard question, expecially if it only asks for odd integers. You do not need to plug in any values and certainly no calculations needed. All you need is a fundamental understanding of what standard deviation means. It is a measure of variation in the set or the distribution of numbers. So without loss of generality if you know the range you can easily enumerate the numbers. Let the 5 dashes below represent the range within which our four integers lie and I will use x's to denote the place of each constituent of the set :      Now, I know the range is 4, so there must be an "x" at the beginning and at the end : x    x I also know all numbers are odd so the other two numbers can only lie on either the first middle or last place giving me the arrangements : xx    xx x  xx  x xx  x  x xxx    x Note that since standard deviation is a second order measure which measures the distribution of numbers it will be exactly the same for the sets "xx  x  x" and "x  x  xx". So we don't need to enumerate symmetric cases Answer is 4
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 07:49
shrouded1 wrote: gurpreetsingh wrote: Very good but time consuming question.
Bunuel do you think it is a Gmat Question.? I dont think this is a hard question, expecially if it only asks for odd integers. You do not need to plug in any values and certainly no calculations needed. All you need is a fundamental understanding of what standard deviation means. It is a measure of variation in the set or the distribution of numbers. So without loss of generality if you know the range you can easily enumerate the numbers. Let the 5 dashes below represent the range within which our four integers lie and I will use x's to denote the place of each constituent of the set :      Now, I know the range is 4, so there must be an "x" at the beginning and at the end : x    x I also know all numbers are odd so the other two numbers can only lie on either the first middle or last place giving me the arrangements : xx    xx x  xx  x xx  x  x xxx    x Note that since standard deviation is a second order measure which measures the distribution of numbers it will be exactly the same for the sets "xx  x  x" and "x  x  xx". So we don't need to enumerate symmetric cases Answer is 4I'd like to clear something for the people who are preparing for GMAT: this might not be a hard question for professional statistician but if such question ever appear on GMAT it'll be considered 750+, so very hard. Usually GMAT SD questions are fairly straightforward and don't require actual calculation of SD, they are about the general understanding of the concept. So don't be scared: it's really unlikely you'll see such a question on GMAT and if you will, then you must know that you are doing very well and are probably very close to 51 on quant.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 08:45
Shrouded, could you elaborate it more.
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London

Re: Hard  standard deviation [#permalink]
Show Tags
01 Oct 2010, 09:47
2
This post received KUDOS
gurpreetsingh wrote: Shrouded, could you elaborate it more. All you need is a fundamental understanding of standard deviation to solve this question, plugging in values is painful and not required. Standard deviation measures how the elements of a set are distributed around the mean, or the "deviation" of the elements in other words. If you have just 4 elements in which the first and last are fixed relative to each other it just boils down to how you can distribute the other two to form different amounts of deviation. The actual enumeration of this is shown above, but all you you need to note is that the deviation is symmetric cases is just the same : {1,1,3,5} {1,3,5,5} OR xx  x  x x  x  xx The deviation is exactly the same, its just the mean which is shifted. Keeping this in mind there are only 4 possibilities with 4 odd numbers of range 4.
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 13 Jul 2010
Posts: 167

oddy integer SD [#permalink]
Show Tags
09 Nov 2010, 17:08
J is a collection of four odd integers whose range is 4. The standard deviation of J must be one of how many numbers?
a 3 b 4 c 5 d 6 e 7
Please explain your thought process on this one. Thanks



Manager
Joined: 30 Sep 2010
Posts: 58

Re: oddy integer SD [#permalink]
Show Tags
09 Nov 2010, 17:22
as range is 4..we know there is a lowest and there is a highest number Now for the rest 2 numbers:
1) either they are equal to lowest number ... >> 1 SD 2) either they are equal to highest number... >> 1 SD 3) either one is equal to lowest number and one is equal to highest number... >> 1 SD 4) they are same but not equal to lowest or highest number... >> 1 SD
So 4 possibilities (please note that all the numbers can not be distinct..otherwise range will be greater than 4)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7446
Location: Pune, India

Re: oddy integer SD [#permalink]
Show Tags
09 Nov 2010, 19:06
gettinit wrote: J is a collection of four odd integers whose range is 4. The standard deviation of J must be one of how many numbers?
a 3 b 4 c 5 d 6 e 7
Please explain your thought process on this one. Thanks This is a good question though I did not like the wording very much. Instead of 'SD of J must be one one how many numbers', 'How many distinct values can SD of J take' is better. Anyway, First I thought J is a set of four odd integers with range 4 so I said J = {1, x, y, 5} Now x and y can take 3 different values: 1, 3 or 5 Either both x and y are same. This can be done in 3 ways. Or x and y are different. This can be done in 3C2 ways = 3 ways Total x and y can take values in 3 + 3 = 6 ways Let me enumerate them for clarification: {1, 1, 1, 5}, {1, 3, 3, 5}, {1, 5, 5, 5}, {1, 1, 3, 5}, {1, 1, 5, 5}, {1, 3, 5, 5} These are the 6 ways in which you can choose the numbers. Important thing: SD of {1, 1, 1, 5} and {1, 5, 5, 5} is same. Why? SD measures distance from mean. It has nothing to do with the actual value of mean and actual value of numbers. In {1, 1, 1, 5}, mean is 2. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. In {1, 5, 5, 5}, mean is 4. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. Similarly, {1, 1, 3, 5} and {1, 3, 5, 5} will have the same SD. Then, {1, 3, 3, 5} will have a distinct SD and {1, 1, 5, 5} will have a distinct SD. In all, there are 4 different values that SD can take in such a case. Note: It doesn't matter what the actual numbers are. SD of 1, 3, 5, 7 is the same as SD of 12, 14, 16, 18. For detailed explanation of SD and how to calculate it, check the theory or Stats.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 13 Jul 2010
Posts: 167

Re: oddy integer SD [#permalink]
Show Tags
15 Nov 2010, 11:41
VeritasPrepKarishma wrote: gettinit wrote: J is a collection of four odd integers whose range is 4. The standard deviation of J must be one of how many numbers?
a 3 b 4 c 5 d 6 e 7
Please explain your thought process on this one. Thanks This is a good question though I did not like the wording very much. Instead of 'SD of J must be one one how many numbers', 'How many distinct values can SD of J take' is better. Anyway, First I thought J is a set of four odd integers with range 4 so I said J = {1, x, y, 5} Now x and y can take 3 different values: 1, 3 or 5 Either both x and y are same. This can be done in 3 ways. Or x and y are different. This can be done in 3C2 ways = 3 ways Total x and y can take values in 3 + 3 = 6 ways Let me enumerate them for clarification: {1, 1, 1, 5}, {1, 3, 3, 5}, {1, 5, 5, 5}, {1, 1, 3, 5}, {1, 1, 5, 5}, {1, 3, 5, 5} These are the 6 ways in which you can choose the numbers. Important thing: SD of {1, 1, 1, 5} and {1, 5, 5, 5} is same. Why? SD measures distance from mean. It has nothing to do with the actual value of mean and actual value of numbers. In {1, 1, 1, 5}, mean is 2. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. In {1, 5, 5, 5}, mean is 4. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. Similarly, {1, 1, 3, 5} and {1, 3, 5, 5} will have the same SD. Then, {1, 3, 3, 5} will have a distinct SD and {1, 1, 5, 5} will have a distinct SD. In all, there are 4 different values that SD can take in such a case. Note: It doesn't matter what the actual numbers are. SD of 1, 3, 5, 7 is the same as SD of 12, 14, 16, 18. For detailed explanation of SD and how to calculate it, check the theory or Stats. Thanks for the great explanations karishma, shrouded, and bunuel as always



Manager
Joined: 14 Nov 2011
Posts: 149
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: Hard  standard deviation [#permalink]
Show Tags
24 May 2013, 18:42
Bunuel wrote: I know this question, I've posted it in my topic: psquestionsaboutstandarddeviation85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear. Hi, in the sets above why aren't sets [3,5,5,5] and [3,3,3,5] considered? Their is no limit on minimum range.



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: Hard  standard deviation [#permalink]
Show Tags
25 May 2013, 03:24
cumulonimbus wrote: Bunuel wrote: I know this question, I've posted it in my topic: psquestionsaboutstandarddeviation85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear. Hi, in the sets above why aren't sets [3,5,5,5] and [3,3,3,5] considered? Their is no limit on minimum range. This cases are not possible since "the greatest difference between any two integers in E is 4" means that the range of the set is 4.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 08 Apr 2012
Posts: 453

Re: Hard  standard deviation [#permalink]
Show Tags
22 Sep 2013, 11:31
Bunuel wrote: cumulonimbus wrote: Bunuel wrote: I know this question, I've posted it in my topic: psquestionsaboutstandarddeviation85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear. Hi, in the sets above why aren't sets [3,5,5,5] and [3,3,3,5] considered? Their is no limit on minimum range. This cases are not possible since "the greatest difference between any two integers in E is 4" means that the range of the set is 4. I have seen that in all previous posts, consideration of sets that are all the same number such as [1,1,1,1] were not considered. Why is that?



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: Hard  standard deviation [#permalink]
Show Tags
23 Sep 2013, 00:58
ronr34 wrote: Bunuel wrote: cumulonimbus wrote: Hi, in the sets above why aren't sets [3,5,5,5] and [3,3,3,5] considered? Their is no limit on minimum range.
This cases are not possible since "the greatest difference between any two integers in E is 4" means that the range of the set is 4. I have seen that in all previous posts, consideration of sets that are all the same number such as [1,1,1,1] were not considered. Why is that? The greatest difference between any two integers in E is 4 means that the range of the set is 4 and the range of {1, 1, 1, 1} is 0, not 4.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 08 Apr 2012
Posts: 453

Re: Hard  standard deviation [#permalink]
Show Tags
30 Oct 2013, 14:38
Bunuel wrote: The greatest difference between any two integers in E is 4 means that the range of the set is 4 and the range of {1, 1, 1, 1} is 0, not 4.
Thanks! I now see it on the post above... must have missed it



Intern
Joined: 21 Jun 2014
Posts: 3

Re: E is a collection of four ODD integers and the greatest [#permalink]
Show Tags
21 Jul 2014, 03:29
Hi
Isn't a set with values 3,3,5, 7 viable??



Math Expert
Joined: 02 Sep 2009
Posts: 39716

Re: E is a collection of four ODD integers and the greatest [#permalink]
Show Tags
21 Jul 2014, 03:36
HarvinderSaini wrote: Hi
Isn't a set with values 3,3,5, 7 viable?? Yes, it is. The sets in my post are based on an assumption that the smallest integer is 1 to simplify finding a pattern. Your set is similar to {1, 1, 3, 5} in my solution.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics




Re: E is a collection of four ODD integers and the greatest
[#permalink]
21 Jul 2014, 03:36



Go to page
1 2
Next
[ 25 posts ]




