It is currently 24 Nov 2017, 06:22

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

There is a set of consecutive even integers. What is the

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

Hide Tags

Manager
Manager
avatar
Joined: 24 May 2010
Posts: 79

Kudos [?]: 61 [0], given: 1

GMAT ToolKit User
There is a set of consecutive even integers. What is the [#permalink]

Show Tags

New post 10 Aug 2010, 08:20
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

56% (00:37) correct 44% (00:34) wrong based on 152 sessions

HideShow timer Statistics

There is a set of consecutive even integers. What is the standard deviation of the set?

(1) There are 39 elements in the set.
(2) the mean of the set is 382.
[Reveal] Spoiler: OA

Kudos [?]: 61 [0], given: 1

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [2], given: 12439

Re: Std [#permalink]

Show Tags

New post 10 Aug 2010, 09:26
2
This post received
KUDOS
Expert's post
Jinglander wrote:
Q: There is a set of consecutive even integers. What is the standard deviation of the set?
(1) There are 39 elements in the set.
(2) the mean of the set is 382.

Answer is a. Can Someone explain

Posted from my mobile device


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:

There is a set of consecutive even integers. What is the standard deviation of the set?

(1) There are 39 elements in the set --> SD of a set of ANY 39 consecutive even integers will be the same, as any set of 39 consecutive even integers can be obtained by adding constant to another set of 39 consecutive integers. For example: set of 39 consecutive integers {4, 6, 8, ..., 80} can be obtained by adding 4 to each term of another set of 39 consecutive integers: {0, 2, 4, ..., 76}. So we can calculate SD of {0, 2, 4, ..., 76} and we'll know that no matter what our set actually is, its SD will be the same. Sufficient.

(2) The mean of the set is 382 --> knowing mean gives us nothing, we must know the number of terms in the set, as SD of {380, 382, 384} is different from SD of {378, 380, 382, 384, 386}. Not sufficient.

Answer: A.

Hope it's clear.
_________________

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 [?]: 133204 [2], given: 12439

Senior Manager
Senior Manager
avatar
Joined: 28 Aug 2010
Posts: 260

Kudos [?]: 793 [0], given: 11

There is a set of consecutive even integers [#permalink]

Show Tags

New post 28 Mar 2011, 19:35
2
This post was
BOOKMARKED
There is a set of consecutive even integers. What is the standard deviation of the set?

(1) There are 39 elements in the set.
(2) the mean of the set is 382.
_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Kudos [?]: 793 [0], given: 11

1 KUDOS received
Director
Director
avatar
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: 03 Feb 2011
Posts: 871

Kudos [?]: 401 [1], given: 123

Reviews Badge
Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 28 Mar 2011, 20:27
1
This post received
KUDOS
Pardon me. Let me try. The sd is a measure of the compactness. The consecutive integers are packed the same way ( equidistant ) from each other no matter where you start counting from. To get the distances from the mean of a data sample you just need the number of elements. Let's say it is 5 and data set is {1 2 3 4 5} the mean is middle number 3. Because of symmetry and knowing data is equidistant from each other, we can calculate the square of individual distances from the mean. Hence we can know the variance. Hence we can get the sd. So here A is sufficient to answer the question. because of symmetry the sd of {1 2 3 4 5} is same as the sd of {96 97 98 99 100} or {11 12 13 14 15} ie any consecutive 5 integers

Posted from my mobile device

Kudos [?]: 401 [1], given: 123

TOEFL Forum Moderator
avatar
Joined: 16 Nov 2010
Posts: 1602

Kudos [?]: 601 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 00:39
To add on top of what gmat1220 has mentioned, assume that you have a set of 39 consecutive even numbers, then the median = mean and thus two numbers on either side of mean will be 2 away, the next two will be 4 away, and so forth. So this gives the number of distances from mean, and the number of terms is already there, so you can substitute and find the SD.( Of course this is a SD question, so no need to calculate any further).


For option 2, there is nothing that gives how the other members of set are placed with respect to mean, or how many numbers are there in the set, and hence there is no definitive answer.

e.g. there could be three members (whereby the SD will be very low), or 100 members, in which case the SD will vary widely as many elements away from the mean will cause the SD to increase.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 601 [0], given: 40

Senior Manager
Senior Manager
avatar
Joined: 28 Aug 2010
Posts: 260

Kudos [?]: 793 [0], given: 11

Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 04:05
thanks a ton guys...ok so statement makes sense, i got that right but my confusion was over statement 2

stmt 2 : it gives us the mean. We already know the that set is set of consecutive even numbers so we know it is evenly distributed so why cant we calculate the SD.

Can someone clarify this.
_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Kudos [?]: 793 [0], given: 11

1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2102 [1], given: 376

Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 04:19
1
This post received
KUDOS
ajit257 wrote:
thanks a ton guys...ok so statement makes sense, i got that right but my confusion was over statement 2

stmt 2 : it gives us the mean. We already know the that set is set of consecutive even numbers so we know it is evenly distributed so why cant we calculate the SD.

Can someone clarify this.


380,382,384. Mean=382. Standard deviation: 2
378,380,382,384,386. Mean=382: Standard deviation: Somewhere between 2 and 4
376,378,380,382,384,386,388; Mean=382: Standard deviation: Somewhere between 4 and 6

Even though the even numbers are symmetrically distributed about the mean, with every inclusion of a pair of numbers, the standard deviation will gradually increase.

380,382,384:
Here there are just two numbers on both sides of 382. The deviation of 380 from the mean 382 is 2; the deviation of 384 from the mean 382 is also 2, thus the standard deviation is 2.

378,380,382,384,386
Here there are 5 numbers.
382 is the mean.
The deviation of 380 from the mean 382 is 2; the deviation of 384 from the mean 382 is also 2;
But,
The deviation of 378 from the mean 382 is 4; the deviation of 384 from the mean 386 is also 4;
Thus the standard deviation will be somewhere between 2 and 4.

Also, as per the rule, the standard deviation increases with increase in the Range of the set.
380,382,384. Range=4
378,380,382,384,386. Range=8
376,378,380,382,384,386,388. Range=12
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 2102 [1], given: 376

Senior Manager
Senior Manager
avatar
Joined: 28 Aug 2010
Posts: 260

Kudos [?]: 793 [0], given: 11

Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 04:37
so stmt 2 is based on the concept of the more numbers you add closer to the mean ....sd changes.

thanks fluke.
_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Kudos [?]: 793 [0], given: 11

Expert Post
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1344

Kudos [?]: 2010 [0], given: 6

Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 10:05
fluke wrote:
380,382,384. Mean=382. Standard deviation: 2


Just to clarify, the standard deviation of that set is not equal to 2. If everything in a set is 2 away from the mean, the standard deviation will indeed be 2, but in your example, 382 is not 2 away from the mean; it is equal to the mean. Because of that, the standard deviation will certainly be less than 2.

If you care to complete the calculation, the distances of the elements in the set {380, 382, 384} to the mean are 2, 0 and 2. Squaring these and averaging, we get 8/3, so the standard deviation is sqrt(8/3).
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 2010 [0], given: 6

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2102 [0], given: 376

Re: Example #2 of SD from gmat math book [#permalink]

Show Tags

New post 29 Mar 2011, 10:14
IanStewart wrote:
fluke wrote:
380,382,384. Mean=382. Standard deviation: 2


Just to clarify, the standard deviation of that set is not equal to 2. If everything in a set is 2 away from the mean, the standard deviation will indeed be 2, but in your example, 382 is not 2 away from the mean; it is equal to the mean. Because of that, the standard deviation will certainly be less than 2.

If you care to complete the calculation, the distances of the elements in the set {380, 382, 384} to the mean are 2, 0 and 2. Squaring these and averaging, we get 8/3, so the standard deviation is sqrt(8/3).


True. My mistake. Thanks.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 2102 [0], given: 376

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15499

Kudos [?]: 283 [0], given: 0

Premium Member
Re: There is a set of consecutive even integers. What is the [#permalink]

Show Tags

New post 02 Oct 2017, 08:38
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 [?]: 283 [0], given: 0

Re: There is a set of consecutive even integers. What is the   [#permalink] 02 Oct 2017, 08:38
Display posts from previous: Sort by

There is a set of consecutive even integers. What is the

  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®.