What is SD of given set of numbers whose average is 5? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 13:33

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is SD of given set of numbers whose average is 5?

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

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 659 [0], given: 15

What is SD of given set of numbers whose average is 5? [#permalink]

### Show Tags

31 Oct 2010, 04:26
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:41) correct 41% (00:39) wrong based on 99 sessions

### HideShow timer Statistics

What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 5 when value of each of the given number is increased by 7
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93353 [1] , given: 10557

Re: Standard Deviation [#permalink]

### Show Tags

31 Oct 2010, 07:40
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
udaymathapati wrote:
What is SD of given set of numbers whose average is 5?
1. None of the numbers are greater than this Average
2. The Standard deviation is 5 when value of each of the given number is increased by 7

Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

We need to know couple of important properties for this question:

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.

Also: If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

That's because if a list contains all identical elements then there is no variation from the mean, hence SD=0.

BACK TO THE ORIGINAL QUESTION:

What is SD of given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average --> if no number is more than the mean then no number is less than mean, which implies that this list contains all identical elements (or which is the same just one element), so SD=0. Sufficient.

(2) The Standard deviation is 0 when value of each of the given number is increased by 7 --> if we add or subtract a constant to each term in a set SD will not change, so SD=0. Sufficient.

For more on Standard Deviation check:
math-standard-deviation-87905.html

Hope it helps.
_________________
Manager
Joined: 09 Jun 2010
Posts: 116
Followers: 2

Kudos [?]: 115 [0], given: 1

Re: Standard Deviation [#permalink]

### Show Tags

31 Oct 2010, 08:06
Something is wrong with this one. I read somewhere that in DS question both the options should give same result if both are sufficient.

From statement:1

Mean = 5 and none of the elements are greater than the mean => all the items in the set are identical therefore the SD = 0; all the items are 5.

Statement: 2

Adding a constant to all the items will not change the SD. Therefore the SD of the original set = 5

The answer is D by the way since both the statements give the SD.
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93353 [0], given: 10557

Re: Standard Deviation [#permalink]

### Show Tags

31 Oct 2010, 08:18
soumanag wrote:
Something is wrong with this one. I read somewhere that in DS question both the options should give same result if both are sufficient.

From statement:1

Mean = 5 and none of the elements are greater than the mean => all the items in the set are identical therefore the SD = 0; all the items are 5.

Statement: 2

Adding a constant to all the items will not change the SD. Therefore the SD of the original set = 5

The answer is D by the way since both the statements give the SD.

You are right: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

There must be a typo in (2) and it should read "The Standard deviation is 0 when ..."
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13487
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: What is SD of given set of numbers whose average is 5? [#permalink]

### Show Tags

25 Nov 2014, 09:15
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 Club Legend
Joined: 09 Sep 2013
Posts: 13487
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: What is SD of given set of numbers whose average is 5? [#permalink]

### Show Tags

24 Jan 2016, 23:04
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: What is SD of given set of numbers whose average is 5?   [#permalink] 24 Jan 2016, 23:04
Similar topics Replies Last post
Similar
Topics:
6 What is the standard deviation of a set of numbers whose mean is 20? 7 21 Sep 2016, 02:56
What is the standard deviation (SD) of the four numbers 1 18 Jun 2013, 21:08
7 The average of 6 numbers in a set is equal to 0. What is the 8 14 Dec 2012, 08:22
3 For a certain set of 3 numbers, is the average 3 27 Feb 2012, 15:50
For a certain set of 3 numbers, is the average 1 15 Jan 2011, 13:33
Display posts from previous: Sort by

# What is SD of given set of numbers whose average is 5?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.