Last visit was: 14 Dec 2024, 00:54 It is currently 14 Dec 2024, 00:54
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,874
Own Kudos:
685,672
 []
Given Kudos: 88,269
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,874
Kudos: 685,672
 []
What is the standard deviation of a set of 7 numbers whose mean is 20? 21 Mar 2017, 05:56
2
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

44% (01:23) correct 56% (01:48) wrong based on 183 sessions

History

Date
Time
Result
Not Attempted Yet
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
A
User avatar
mvictor
User avatar
Board of Directors
Joined: 17 Jul 2014
Last visit: 14 Jul 2021
Posts: 2,136
Own Kudos:
1,219
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Products:
My Reviews
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
Posts: 2,136
Kudos: 1,219
What is the standard deviation of a set of 7 numbers whose mean is 20? 21 Mar 2017, 06:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
since there are 7 numbers in the set, I believe it's A.
all numbers are 20, thus, SD is 0
were there 2, 4, 6, 8 numbers - i think it would have been E.
User avatar
mohshu
User avatar
Joined: 21 Mar 2016
Last visit: 26 Dec 2019
Posts: 448
Own Kudos:
127
Given Kudos: 103
Products:
My Reviews
Posts: 448
Kudos: 127
What is the standard deviation of a set of 7 numbers whose mean is 20? 21 Mar 2017, 22:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
first lets understand how SD is calculated..

stat 1: it says absolute value is same. but no information about abs value is given.
hence not suff

stat 2: it only says sum is greater than 100.. it can be 110, 120 ,,anything above 100..not suff

both combined not suff.

hence E
User avatar
nhurmade
User avatar
Joined: 05 Nov 2016
Last visit: 27 Nov 2017
Posts: 2
Own Kudos:
6
Given Kudos: 7
Location: India
GMAT 1: 680 Q49 V32
GMAT 2: 630 Q49 V26
GMAT 2: 630 Q49 V26
Posts: 2
Kudos: 6
What is the standard deviation of a set of 7 numbers whose mean is 20? 30 Oct 2017, 00:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please elaborate How is only A sufficient?

I thought for it the following way:
(A) given that the difference from mean is same, means SD is one fixed value. for example, the {15,15,15,20,25,25,25} with sd=5 OR {10,10,10,20,30,30,30} with sd=10
standard deviation is variable, hence not sufficient.

(B) the sum greater than 100 could be anything, 101 or 500 or 5000.
Hence, not sufficient.

The correct answer seems to be E.
Please correct me if wrong.
User avatar
chetan2u
User avatar
RC & DI Moderator
Joined: 02 Aug 2009
Last visit: 13 Dec 2024
Posts: 11,434
Own Kudos:
38,028
 []
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert reply
Posts: 11,434
Kudos: 38,028
 []
What is the standard deviation of a set of 7 numbers whose mean is 20? 30 Oct 2017, 09:50
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.


Hi...
there has been some confusion over the solution, so let me pitch in..

there are 7 numbers and mean is 20

lets see the statements-

(1) The absolute value of the difference of each number in the set from the mean is equal.
Since it talks of EACH number from mean is equal, the first thing you should realize is that MEAN is NOT in the set if numbers are different OR all are equal to mean
lets see these two cases-
A) All are equal to MEAN that is 20 so 20,20,20,20,20,20,20... SD will be 0
B) Mean is not in the set - Since there are ODD elements in the set, MEAN will never be 20..
say 3 are 1 above mean, the other 3 will cover up by being 1 below mean but what about 7th - it has to be EQUAL to mean to keep the mean as 20
as per statement I , set will be 19,19,19,19,21,21,21 or 19,19,19,21,21,21,21 but in each case mean will not be 20
so ONLY possibility is 20,20,20,20,20,20,20 and SD will be 0...
suff


(2) The sum of the squares of the differences from the mean is greater than 100.
clearly insuff

A
User avatar
nhurmade
User avatar
Joined: 05 Nov 2016
Last visit: 27 Nov 2017
Posts: 2
Own Kudos:
6
 []
Given Kudos: 7
Location: India
GMAT 1: 680 Q49 V32
GMAT 2: 630 Q49 V26
GMAT 2: 630 Q49 V26
Posts: 2
Kudos: 6
 []
What is the standard deviation of a set of 7 numbers whose mean is 20? 30 Oct 2017, 10:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks chetan2u!
I think i understood it now. I need to read the question very carefully and pay attention to the words. Thanks again!
User avatar
hellosanthosh2k2
User avatar
Joined: 02 Apr 2014
Last visit: 07 Dec 2020
Posts: 366
Own Kudos:
525
Given Kudos: 1,227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Schools: XLRI"20
GMAT 1: 700 Q50 V34
Posts: 366
Kudos: 525
What is the standard deviation of a set of 7 numbers whose mean is 20? 09 Nov 2017, 12:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
Bunuel
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.


Hi...
there has been some confusion over the solution, so let me pitch in..

there are 7 numbers and mean is 20

lets see the statements-

(1) The absolute value of the difference of each number in the set from the mean is equal.
Since it talks of EACH number from mean is equal, the first thing you should realize is that MEAN is NOT in the set if numbers are different OR all are equal to mean
lets see these two cases-
A) All are equal to MEAN that is 20 so 20,20,20,20,20,20,20... SD will be 0
B) Mean is not in the set - Since there are ODD elements in the set, MEAN will never be 20..
say 3 are 1 above mean, the other 3 will cover up by being 1 below mean but what about 7th - it has to be EQUAL to mean to keep the mean as 20
as per statement I , set will be 19,19,19,19,21,21,21 or 19,19,19,21,21,21,21 but in each case mean will not be 20
so ONLY possibility is 20,20,20,20,20,20,20 and SD will be 0...
suff


(2) The sum of the squares of the differences from the mean is greater than 100.
clearly insuff

A

Hi chetan2u Bunuel

Statement 1, difference between any value and mean is equal. This is possible only when all the elements in the set are same. So SD = sq.root of (sum of squares of differences of each value from mean)/7 = 0 -> sufficient.

However, statement 2, says sum of squares of differences of each value from mean > 100. I am not sure how it is possible.
From statement 1, we get all elements are same, but statement2 is contradicting.

So i was scratching my head

Please help.
avatar
yhu08902
avatar
Joined: 14 Sep 2018
Last visit: 04 Jan 2022
Posts: 20
Own Kudos:
3
Given Kudos: 16
Location: United States (NJ)
Concentration: Finance, Strategy
Schools: Wharton Exec '21 (A)
GMAT 1: 680 Q50 V31
GPA: 3.87
WE:Business Development (Insurance)
Schools: Wharton Exec '21 (A)
GMAT 1: 680 Q50 V31
Posts: 20
Kudos: 3
What is the standard deviation of a set of 7 numbers whose mean is 20? 11 Oct 2018, 19:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

I chose E at first, but would agree A is correct answer. Note that (1) says "The absolute value of the difference of each number in the set from the mean is equal." , the value of the difference of each number from the mean has to be 0, i.e., all 7 numbers are 20, thus SD is 0.
avatar
anmolsd1995
avatar
Joined: 17 Apr 2017
Last visit: 12 Dec 2021
Posts: 11
Own Kudos:
3
Given Kudos: 26
Posts: 11
Kudos: 3
What is the standard deviation of a set of 7 numbers whose mean is 20? 08 Feb 2019, 07:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nhurmade
Please elaborate How is only A sufficient?

I thought for it the following way:
(A) given that the difference from mean is same, means SD is one fixed value. for example, the {15,15,15,20,25,25,25} with sd=5 OR {10,10,10,20,30,30,30} with sd=10
standard deviation is variable, hence not sufficient.

(B) the sum greater than 100 could be anything, 101 or 500 or 5000.
Hence, not sufficient.

The correct answer seems to be E.
Please correct me if wrong.

I have this same doubt can anyone explain ?
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 579
Own Kudos:
424
Given Kudos: 596
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 579
Kudos: 424
What is the standard deviation of a set of 7 numbers whose mean is 20? 08 Jul 2019, 19:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma

Can you please chip in and explain in detail??
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 13 Dec 2024
Posts: 15,546
Own Kudos:
70,245
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,546
Kudos: 70,245
What is the standard deviation of a set of 7 numbers whose mean is 20? 11 Jul 2019, 03:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
warrior1991
VeritasKarishma

Can you please chip in and explain in detail??

Can you tell me exactly where the question appears in our curriculum? The way it is given here, there is a problem in the question. It has contradictory statements. I need to check at the source.
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 579
Own Kudos:
424
Given Kudos: 596
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 579
Kudos: 424
What is the standard deviation of a set of 7 numbers whose mean is 20? 11 Jul 2019, 19:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
warrior1991
VeritasKarishma

Can you please chip in and explain in detail??

Can you tell me exactly where the question appears in our curriculum? The way it is given here, there is a problem in the question. It has contradictory statements. I need to check at the source.

NO other place . Check the tag "Veritas Prep" . Since it was posted by Bunuel, I thought that it may be coming from Veritas Prep.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
Bunuel
Math Expert
97874 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3116 posts
GMATBusters
GMAT Tutor
1930 posts