Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Oct 2014, 15:58

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

S and T are sets of numbers. The standard deviation of the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 132 [0], given: 0

S and T are sets of numbers. The standard deviation of the [#permalink] New post 22 Jul 2006, 04:31
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 132 [0], given: 0

 [#permalink] New post 22 Jul 2006, 08:03
Note: U means union
Manager
Manager
avatar
Joined: 07 Jul 2005
Posts: 65
Followers: 1

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

 [#permalink] New post 22 Jul 2006, 08:40
Quote:
The range of S U T is different from the range of S.


If range of union is different then standard deviation will also defer.

My answer is A
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 132 [0], given: 0

 [#permalink] New post 22 Jul 2006, 12:47
capri wrote:
Quote:
The range of S U T is different from the range of S.


If range of union is different then standard deviation will also defer.

My answer is A


It certainly differs, but read the question carefully
Senior Manager
Senior Manager
avatar
Joined: 09 Aug 2005
Posts: 286
Followers: 1

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

Re: DS: Two sets [#permalink] New post 22 Jul 2006, 13:02
kevincan wrote:
S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.


1. range differs means it can only increase therefore SD increases

suff

2. one element is 2times more than mean - therefore sd increases ---SD will not increase if the lone element in T is equal to the mean


So D
Director
Director
User avatar
Joined: 28 Dec 2005
Posts: 761
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: DS: Two sets [#permalink] New post 22 Jul 2006, 14:05
kevincan wrote:
S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.



going with C.

Just starting out with math, so am just trying to nail down the concepts.

1: The range can only change in a set if the difference between the greatest elements in the set changes. Since the new set SUT contains all the elements of the old set S, the range of the new set, if different, must be greater, since it cannot be smaller. However we are concerned not with range but with SD. There may be 5 elements in S and 1000 elements in T. One element in T is greater than the largest elememt in S or lesser than the smallest in S, increasing the range. This one element will certainly cause the SD to increase. The other 999 elements may actually be the same value as the arithmetic mean, thereby reducing the SD.

We cannot say from 1, if the SD will increase or decrease, though we can say that the range will increase.


2: There is a single element in T which is twice the average. Consider a set as follows:-

{ 0, 10000}

Now add another element which is twice the mean, i.e. 10000
Since the question does not say the sets are disjoint, this is possible.
Set SUT = S = { 0, 10000 }, and the SD does not change.

Consider another set S {0,10,20} mean = 10, SD = 5.something.
Add an element twice the mean i.e. 20. SD increases.
Therefore 2 is incufficient.

Consider 1 and 2 together. If there is one element added, and this causes the range to increase, it cannot be an element already in S. Then, SD will increase.

Will go with C
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2922
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 15

Kudos [?]: 81 [0], given: 0

 [#permalink] New post 22 Jul 2006, 14:06
C

St1: If range increases then SD may increase or decrease depending on how the mean is affected. Data points may lie farther than mean or closer to mean. INSUFF

St2: That one point may increase or decrease the range and can also increase or decrease the mean.: INSUFF
Case1: S = {-1,0,0,0,1} Mean = 0 So T = {0}
Variance of S = 2/4
Variance of T = 0
Variance of (S and T) = 2/5

Case2: S = {2,2,2,2} means = 2 so T = {4}
Variance of S = 0
Variance of T = 0
Variance of (S and T) is greater than 0 because mean is 12/5 and more points are far scattered to mean.

Combined:

It means one point of T will increase the rangle of (S and T) and will increase the SD.
Case1 of statement is out and case 2 is in. that means SD will increase.

NOTE: Variance = SD^2
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1497
Followers: 6

Kudos [?]: 31 [0], given: 0

Re: DS: Two sets [#permalink] New post 23 Jul 2006, 10:43
kevincan wrote:
S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.


its B for me.

1. difference in range could increase or decrease the SD. nsf.
2. if T has only one element, then S U T has either 1 or 0 element (since we know from the question that set S has more than 1 element). in both cases the SD is 0. so suff.
Senior Manager
Senior Manager
User avatar
Joined: 20 Feb 2006
Posts: 331
Followers: 1

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

Re: DS: Two sets [#permalink] New post 23 Jul 2006, 21:57
kevincan wrote:
S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.




Will go with B.. B tells that we adding another element that's twice the mean.
This means we are adding square of mean to variance.. This means standard deviation will increase..

Just B..
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 132 [0], given: 0

 [#permalink] New post 23 Jul 2006, 23:52
Why are (1) and (2) sufficient together?
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2251
Followers: 12

Kudos [?]: 203 [0], given: 0

 [#permalink] New post 24 Jul 2006, 06:43
If the range of SUT is same with S then it means we are adding one point (T) within the range of S. The points are less scattered. In other words SD would become smaller.

If the range of SUT is different from S then it means we are adding one point (T) outside the range of S. The points are more scattered. In other words SD would be greater.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

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

 [#permalink] New post 24 Jul 2006, 08:56
E.

A is not sufficient.
I only present an example, in which q decreases: T=(1, 1, 1, 1, 1, 1, 1,1 ....,1) 1*10^12 times; S=(4, 8, 12). Then the standard deviation surely decreases.

B. is not sufficient too.
For example:
S=(0,0,0) T=0. Then q does not increase.
(examples, where q increases are easy to find)

Both statements together are not sufficient.

[Note: It is sufficient to find an example and a counterexample; this sketch is not necessary)

To provide a general insight is somewhat complicated (I can't use symbols here).

Sketch:
We are able to compute the new average (na).
Consider the formula of the new standard deviation:
1/(n+1)*sum(x(i) - x(bar))^2 = 1/(n+1)*sum((x(j)-x(bar))^2)+1/(n+1)*x(bar)^2 = ...
We can compare this term with the old term.
The new standard deviation could be smaller or bigger than the old st. d (just plug-in some numbers).

OE (Short-Cut)?
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1269
Location: Madrid
Followers: 23

Kudos [?]: 132 [0], given: 0

 [#permalink] New post 24 Jul 2006, 10:38
Yours will do, though with a simpler counterexample:

Any set made up of many slightly postive numbers and one large negative number, a set that has a mean that is slightly positive, too.

Ex The 9-element set (-3,1.5,1.5,1.5,...,1.5) mean 1
variance (4^2+ 8(0.5)^2)/9= 2

If we include the element 2 (twice the mean of S), new mean is 1.1

variance= ((4.1)^2+8(0.4)^2+ (0.9)^2)/10 which is less than (17+1.3+1)/10, which is less than 2.

Admittedly, this is not a fair question, but a lot of people fell for A, which is disconcerting! OA=E
  [#permalink] 24 Jul 2006, 10:38
    Similar topics Author Replies Last post
Similar
Topics:
standard deviation-set of integers dimri10 3 26 Jun 2011, 06:10
Is the standard deviation of set S greater than the standard amitdgr 7 01 Nov 2008, 07:52
Q is a set of 10 numbers. What is the standard deviation of gmat blows 3 09 Jan 2008, 16:33
Is the Standard Deviation of Set S greater than Standard mitul 2 27 Sep 2006, 17:35
S and T are sets of numbers. The standard deviation of the yezz 4 13 Aug 2006, 02:12
Display posts from previous: Sort by

S and T are sets of numbers. The standard deviation of the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.