BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Manhattan GMAT - Standard Deviation

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
GMAT Score:640

by GmatKiss » Mon May 21, 2012 5:24 am
Question frame:

Does consecutive integers mean the following,

1,2,3,4 ....
13,14,15,16,...

If so, answer should be D.

1) S.D is 1
2) S.D is 1

If consecutive integers mean,

1,2,3,4,5,.... and also
5,10,15,20,... and also
12,24,36,48,...

Then answer will be E

P:S. I have seen MGMAT Forum stating A as the answer.
Please help me if i am missing something basic here!

TIA,
GK
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon May 21, 2012 5:49 am
krishna239455 wrote:If Q is 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
SD describes how much a set of data DEVIATES from the mean.

Statement 1: Set Q contains 21 terms.
Any set of 21 consecutive integers will deviate from the mean exactly the same way.
Thus, the SD can be determined.
SUFFICIENT.

Statement 2: Median = 20.
With evenly spaced numbers, mean = median.
Thus, the mean of the set is 20.
But without knowing the number of terms, we can't determine how much the set DEVIATES from the mean.
If there is only one term -- if Q = {20} -- then there is NO deviation from the mean.
If there are 101 terms, then there is quite a bit of deviation from the mean.
Thus, the SD can be different values.
INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Sun Oct 30, 2011 6:52 pm

by ubhanja » Tue May 22, 2012 10:19 am
how can this be A? This has to be C.

A - Tells that it can be determined. But we don't know the exact value till we combine both the statements. Please clarify.
Top
Master | Next Rank: 500 Posts
Posts: 152
Joined: Mon Feb 20, 2012 12:56 pm
Location: New york
Thanked: 9 times

by agarwalva » Tue May 22, 2012 2:26 pm
ubhanja wrote:how can this be A? This has to be C.

A - Tells that it can be determined. But we don't know the exact value till we combine both the statements. Please clarify.
example
consider list 1 , 2, 3, 4, 5 [5 consecutive integers]
mean is 3.
(1-3)^2 = 4 (5-3)^2 = 4
(2-3)^ = 1 (4-3)^2 = 1
(3-3)^2 = 0
SD = SqRoot (4+1+01+4)/5 = 2


Now another list 6,7,8,9,10
Mean is 8

(6-8)^2 = 4 (10-8)^2 = 4
(7-8)^2 = 1 (9-8)^2= 1
(8-8)^2 = 0

SD = SqRoot (4+1+01+4)/5 = 2

Standard deviation in case of any 5 consecutive integers is 2. Similarly SD in case of any 21 consecutive integers is same.
We just need the number of terms.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 181
Joined: Fri Feb 17, 2012 9:36 am
Thanked: 1 times
Followed by:1 members
GMAT Score:620

by heymayank08 » Tue May 22, 2012 5:53 pm
GMATGuruNY wrote:
krishna239455 wrote:
Statement 2: Median = 20.
With evenly spaced numbers, mean = median.
Thus, the mean of the set is 20.
But without knowing the number of terms, we can't determine how much the set DEVIATES from the mean.
If there is only one term -- if Q = {20} -- then there is NO deviation from the mean.
If there are 101 terms, then there is quite a bit of deviation from the mean.
Thus, the SD can be different values.
INSUFFICIENT.

The correct answer is A.
mitch but it is written that Q is a set of consecutive itegers so there ought to be more than one integer in the set..
isn't it???
pls correct me if i am wrong.. :)
Top
User avatar
Legendary Member
Posts: 1325
Joined: Sun Nov 01, 2009 6:24 am
Thanked: 105 times
Followed by:14 members

by vikram4689 » Tue May 22, 2012 6:09 pm
Standard deviation means how much the values in a set differ from the mean value. To calculate we need range of integers and integers itself.

A gives us total numbers = 21 and consecutive integers means difference = 1 so we can form a sequence. Remembers S.D. does not vary by adding or subtracting a particular no. to all members of a set, so we need relative value as given in option A.

B says median is 20 but what about range 19,20,21 OR 18,19,20,21,22 ...both have different S.D. as they have different range.

Answer is A
Premise: If you like my post
Conclusion : Press the Thanks Button ;)
Top
User avatar
Legendary Member
Posts: 626
Joined: Fri Dec 23, 2011 2:50 am
Location: Ahmedabad
Thanked: 31 times
Followed by:10 members

by ronnie1985 » Wed May 23, 2012 7:02 am
Std dev = root mean square of deviations from mean

If the set starts from a and ends in a+n-1 containing n terms,

mean = a+(n-1)/2

dev1 = -(n-1)/2
dev2 = 1-(n-1)/2
dev3 = 2-(n-1)/2
.
.
.
devn = n-1-(n-1)/2

Hence the sum of squares of deviations will also be a function of n only. It is independent of a, the first term.

Hence number of terms is sufficient to find the std deviation of an AP.

S1 Gives no of terms hence sufficient

S2 gives median hence not sufficient

(A) is the answer
Follow your passion, Success as perceived by others shall follow you
Top
Post new topic Post Reply
• Page 1 of 1