Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Status: Dedicates 2013 to MBA !!
Joined: 06 Jul 2012
Posts: 32
Location: United States (MI)
Concentration: Entrepreneurship, General Management
GPA: 3.8
WE: Information Technology (Consulting)

If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
Updated on: 15 Aug 2014, 09:10
Question Stats:
54% (00:54) correct 46% (00:59) wrong based on 454 sessions
HideShow timer Statistics
If Q is a set of consecutive integers, what is the standard deviation of Q? (1) Set Q contains 21 terms. (2) The median of set Q is 20. Official explanation from the Manhattan GMAT1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x:
[x – 10, x – 9, x – 8, x – 7, x – 6, x – 5, x – 4, x – 3, x – 2, x – 1, x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7, x + 8, x + 9, x + 10]
Notice that the difference between the mean (x) and the first term in the set (x – 10) is 10. The difference between the mean (x) and the second term in the set (x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set!
(The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation:
Sum of the squared differences: 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 + 02 + (1)2 + (2)2(3)2 + (4)2 + (5)2 + (6)2(7)2 + (8)2 + (9)2 + (10)2 = 770 Average of the sum of the squared differences:
770/21 = 36 2/3
The square root of this average is the standard deviation: ≈ 6.06
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Thanks and Regards, Charu Kapoor
Never Never Never GIVE UP !! Consider KUDOS in case I was able to help you.
Originally posted by CharuKapoor on 28 Apr 2013, 08:30.
Last edited by Bunuel on 15 Aug 2014, 09:10, edited 2 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 55635

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 00:33
Two very important properties of standard deviation: If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change.
If we increase or decrease each term in a set by the same percent (multiply all terms by the constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent.You can try it yourself: SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set. That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant. Back to the original question:If Q is a set of consecutive integers, what is the standard deviation of Q?(1) Set Q contains 21 terms > SD of ALL sets with 21 consecutive integers will be the same, as any set of 21 consecutive integers can be obtained by adding constant to another set of 21 consecutive integers. For example: set of 21 consecutive integers {4, 5, 6, ..., 24} can be obtained by adding 4 to each term of another set of 21 consecutive integers: {0, 1, 2, ..., 20}. So we can calculate SD of {0, 1, 2, ..., 20} and we'll know that no matter what our set actually is, its SD will be the same. Sufficient. (2) The median of set Q is 20. Clearly insufficient. Answer: A. Hope it's clear.
_________________




VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1048
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
28 Apr 2013, 08:37
If Q is a set of consecutive integers, what is the standard deviation of Q?(1) Set Q contains 21 terms.The integers are consecutives, the first value has no importance in the stdDev. If we know that there are 21 integers, they will be in the form x,x+1,x+2,...,x+20. We can locate the middle value and we know "how far" each value is. Sufficient (2) The median of set Q is 20.Example: a set of {19 20 21} or a set of {18 19 20 21 22} both have median 20 but the stdDev in the latter is bigger. Not sufficient A
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 607

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
28 Apr 2013, 08:46
CharuKapoor wrote: If Q is a set of consecutive integers, what is the standard deviation of Q? (1) Set Q contains 21 terms. (2) The median of set Q is 20. Friends, I encountered this one on MGMAT test and initially got it wrong. Let's discuss. From the F.S 1,consider the series [10,8,9......0,1,2,3....9,10]. We have a fixed value for the S.D for the given series. Also, S.D. doesn't change if we add a constant across. Thus, we could add a constant 'a' to the above series > The value of S.D will not change, irrespective the value of a.Sufficient. From F.S 2, all we know is that the median is 20 and the series is of consecutive integers. For 19,20,21 the S.D would be different than that for 18,19,20,21,22.Insufficient. A.
_________________



Manager
Joined: 04 Sep 2012
Posts: 128

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 01:24
Bunuel just one question what will be the SD of a set of (10, 9 ,......0....9,10) and what will be the SD of (1,2,......20,21)..Also ranges of both sets. Sorry for asking stupid questions but it confused me here. Thanks, Abhinav
_________________
Regards, Abhinav
GMAT 1  580 (Q47 V23) http://gmatclub.com/forum/atightslaponface149457.html
GMAT 2  670 (Q48 V34) http://gmatclub.com/forum/670onemonthofffromofficeand2monthshardwork163761.html#p1297561
“If you don't change your life; your life will change you.”



Math Expert
Joined: 02 Sep 2009
Posts: 55635

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 01:39
abhinav11 wrote: Bunuel just one question what will be the SD of a set of (10, 9 ,......0....9,10) and what will be the SD of (1,2,......20,21)..Also ranges of both sets.
Sorry for asking stupid questions but it confused me here.
Thanks, Abhinav The two sets {10, 9, ..., 10} and {1, 2, ..., 21} have the same standard deviation and the same range: SD = \(\sqrt{\frac{110}{3}}\); RANGE = (largest)(smallest) = 10(10) = 20 or 211=20.
_________________



Intern
Status: Dedicates 2013 to MBA !!
Joined: 06 Jul 2012
Posts: 32
Location: United States (MI)
Concentration: Entrepreneurship, General Management
GPA: 3.8
WE: Information Technology (Consulting)

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 06:10
Thanks everyone who took initiative to explain. I'm also posting an explanation from Manhattan GMAT and I hope none of us will get this or any other Standard Deviation Question wrong in future.  The procedure for finding the standard deviation for a set is as follows: 1) Find the difference between each term in the set and the mean of the set. 2) Average the squared "differences." 3) Take the square root of that average. Notice that the standard deviation hinges on step 1: finding the difference between each term in the set and the mean of the set. Once this is done, the remaining steps are just calculations based on these "differences." Thus, we can rephrase the question as follows: "What is the difference between each term in the set and the mean of the set?" (1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x: [x – 10, x – 9, x – 8, x – 7, x – 6, x – 5, x – 4, x – 3, x – 2, x – 1, x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7, x + 8, x + 9, x + 10] Notice that the difference between the mean (x) and the first term in the set (x – 10) is 10. The difference between the mean (x) and the second term in the set (x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set! (The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation: Sum of the squared differences: 10^2 + 9^2 + 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2 + 0^2 + (1)^2 + (2)^2 + (3)^2 + (4)^2 + (5)^2 + (6)^2 + (7)^2 + (8)^2 + (9)^2 + (10)^2 = 770 Average of the sum of the squared differences: 770/21 = 36 2/3 The square root of this average is the standard deviation: ≈ 6.06 (2) NOT SUFFICIENT: Since the set is consecutive, we know that the median is equal to the mean. Thus, we know that the mean is 20. However, we do not know how big the set is so we cannot identify the difference between each term and the mean. Therefore, the correct answer is A.
_________________
Thanks and Regards, Charu Kapoor
Never Never Never GIVE UP !! Consider KUDOS in case I was able to help you.



Manager
Joined: 04 Sep 2012
Posts: 128

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 08:52
CharuKapoor wrote: Thanks everyone who took initiative to explain. I'm also posting an explanation from Manhattan GMAT and I hope none of us will get this or any other Standard Deviation Question wrong in future.  The procedure for finding the standard deviation for a set is as follows: 1) Find the difference between each term in the set and the mean of the set. 2) Average the squared "differences." 3) Take the square root of that average. Notice that the standard deviation hinges on step 1: finding the difference between each term in the set and the mean of the set. Once this is done, the remaining steps are just calculations based on these "differences." Thus, we can rephrase the question as follows: "What is the difference between each term in the set and the mean of the set?" (1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x: [x – 10, x – 9, x – 8, x – 7, x – 6, x – 5, x – 4, x – 3, x – 2, x – 1, x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7, x + 8, x + 9, x + 10] Notice that the difference between the mean (x) and the first term in the set (x – 10) is 10. The difference between the mean (x) and the second term in the set (x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set! (The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation: Sum of the squared differences: 10^2 + 9^2 + 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2 + 0^2 + (1)^2 + (2)^2 + (3)^2 + (4)^2 + (5)^2 + (6)^2 + (7)^2 + (8)^2 + (9)^2 + (10)^2 = 770 Average of the sum of the squared differences: 770/21 = 36 2/3 The square root of this average is the standard deviation: ≈ 6.06 (2) NOT SUFFICIENT: Since the set is consecutive, we know that the median is equal to the mean. Thus, we know that the mean is 20. However, we do not know how big the set is so we cannot identify the difference between each term and the mean. Therefore, the correct answer is A. Sorry but this is way too complex to do in timed environment
_________________
Regards, Abhinav
GMAT 1  580 (Q47 V23) http://gmatclub.com/forum/atightslaponface149457.html
GMAT 2  670 (Q48 V34) http://gmatclub.com/forum/670onemonthofffromofficeand2monthshardwork163761.html#p1297561
“If you don't change your life; your life will change you.”



Intern
Status: Dedicates 2013 to MBA !!
Joined: 06 Jul 2012
Posts: 32
Location: United States (MI)
Concentration: Entrepreneurship, General Management
GPA: 3.8
WE: Information Technology (Consulting)

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
29 Apr 2013, 12:04
Hi Abhinav, One actually need not do all this calculation. The reason I posted the explanation is because, understanding the concept of Standard Deviation will help us tackle all other questions on this topic. GMAT tricks us by combining things such as  Standard Deviation and other concepts of statistics with Data Sufficiency. In case you need further explanation, kindly let me know.
_________________
Thanks and Regards, Charu Kapoor
Never Never Never GIVE UP !! Consider KUDOS in case I was able to help you.



CEO
Joined: 12 Sep 2015
Posts: 3777
Location: Canada

Re: If Q is a set of consecutive integers, what is the standard deviation
[#permalink]
Show Tags
20 Dec 2016, 16:11
amandeep_k wrote: If Q is a set of consecutive integers, what is the standard deviation of Q?
(1) Set Q contains 21 terms.
(2) The median of set Q is 20. Target question: What is the standard deviation of Q? Given: Q is a set of CONSECUTIVE integers Statement 1: Set Q contains 21 terms. NOTE: Standard Deviation measures dispersion (spreadapartness). As such, the actual values mean nothing compared to RELATIVE values. For example, the set {1,2,3,4} has the SAME STANDARD DEVIATION as the set {6,7,8,9} So, knowing that set Q consists of 21 CONSECUTIVE integers is SUFFICIENT. The Standard Deviation of Q will be the same as the Standard Deviation of {1,2,3,4...20,21} Statement 2: The median of set Q is 20. There are several different sets that satisfy this condition. For example, set Q could equal {19, 20, 21} or set Q could equal {18, 19, 20, 21, 22} These two sets have DIFFERENT standard deviations. So, statement 2 is NOT SUFFICIENT Answer: A
_________________
Test confidently with gmatprepnow.com



Director
Joined: 12 Nov 2016
Posts: 715
Location: United States
GPA: 2.66

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
13 Jul 2017, 16:50
CharuKapoor wrote: If Q is a set of consecutive integers, what is the standard deviation of Q? (1) Set Q contains 21 terms. (2) The median of set Q is 20. Official explanation from the Manhattan GMAT1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x:
[x – 10, x – 9, x – 8, x – 7, x – 6, x – 5, x – 4, x – 3, x – 2, x – 1, x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7, x + 8, x + 9, x + 10]
Notice that the difference between the mean (x) and the first term in the set (x – 10) is 10. The difference between the mean (x) and the second term in the set (x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set!
(The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation:
Sum of the squared differences: 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 + 02 + (1)2 + (2)2(3)2 + (4)2 + (5)2 + (6)2(7)2 + (8)2 + (9)2 + (10)2 = 770 Average of the sum of the squared differences:
770/21 = 36 2/3
The square root of this average is the standard deviation: ≈ 6.06 You don't actually have to know what the median value of the set is because if you know the number of terms and the common difference like in this sequence then you can know the s.d x2, x1 ,x, x+1 .. etc



Director
Joined: 12 Nov 2016
Posts: 715
Location: United States
GPA: 2.66

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
10 Sep 2017, 23:17
CharuKapoor wrote: If Q is a set of consecutive integers, what is the standard deviation of Q? (1) Set Q contains 21 terms. (2) The median of set Q is 20. Official explanation from the Manhattan GMAT1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x:
[x – 10, x – 9, x – 8, x – 7, x – 6, x – 5, x – 4, x – 3, x – 2, x – 1, x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7, x + 8, x + 9, x + 10]
Notice that the difference between the mean (x) and the first term in the set (x – 10) is 10. The difference between the mean (x) and the second term in the set (x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set!
(The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation:
Sum of the squared differences: 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 + 02 + (1)2 + (2)2(3)2 + (4)2 + (5)2 + (6)2(7)2 + (8)2 + (9)2 + (10)2 = 770 Average of the sum of the squared differences:
770/21 = 36 2/3
The square root of this average is the standard deviation: ≈ 6.06 The SD is only restricted by the number of terms so we just need to know the number of terms St 1 gives us this exactly suff St 2 clearly insuff A



NonHuman User
Joined: 09 Sep 2013
Posts: 11376

Re: If Q is a set of consecutive integers, what is the standard
[#permalink]
Show Tags
13 Sep 2018, 05:43
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: If Q is a set of consecutive integers, what is the standard
[#permalink]
13 Sep 2018, 05:43






