GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 20:53

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

Standard Deviation Formula

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

Hide Tags

Intern
Intern
avatar
Joined: 10 Aug 2013
Posts: 14
Location: United States
Standard Deviation Formula  [#permalink]

Show Tags

New post 28 Mar 2015, 21:34
1
How can we calculate S.D if we know number of terms ,n, and that the series of numbers is consecutive.
I remember there is a direct formula.Can someone pls share it.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Standard Deviation Formula  [#permalink]

Show Tags

New post 28 Mar 2015, 22:40
Hi AIMGMAT770,

The GMAT is NEVER going to ask you to calculate Standard Deviation, so you don't need to know the formula to do so; instead, you'll be tested on your general knowledge of the concept and the ideas that it is based on. It's not a big subject on Test Day (you'll likely see just 1 question on it). The basic premise in most SD questions is about how "spread out" a group of numbers is, how to raise/lower the SD of the group or some type of general comparison (eg. which group has the higher SD).

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Director
Director
User avatar
B
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 604
Re: Standard Deviation Formula  [#permalink]

Show Tags

New post 30 Mar 2015, 23:15
1
AIMGMAT770

I have attached a snippet on Standard Deviation from the Official Guide to GMAT. You can use this approach to compute standard deviation for any set of numbers. GMAT in general does not ask you to compute standard deviation of a set of numbers, however if they do ask you to compute it then they will give you the formula for standard deviation(they have tested it) and you do need to know how to use it. The example given in the Official Guide should be enough to take on any computation problem on the GMAT.

What is more important is to understand the conceptual meaning of standard deviation. For example, the case of consecutive integers is interesting. What is the standard deviation of five consecutive integers? Does it depend on the specific set of consecutive integers, meaning do these two sets: {1,2,3,4,5} and {13,14,15,16,17}, have different standard deviations. You should be able to answer this question once you conceptually understand what standard deviation is all about. You will also need to know how the average of a set of consecutive integers is related to the numbers in the set.

My advice is not to worry about memorizing special cases, but instead to have the ability to deal with them as needed.
Attachments

StdDeviationGMAT.png
StdDeviationGMAT.png [ 88.36 KiB | Viewed 1920 times ]

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2069
Standard Deviation Formula  [#permalink]

Show Tags

New post 18 Apr 2015, 06:28
AIMGMAT770 wrote:
How can we calculate S.D if we know number of terms ,n, and that the series of numbers is consecutive.
I remember there is a direct formula.Can someone pls share it.


Dear AIMGMAT770,

As has already been pointed above, you're not going to see a PS question of the type:

'What is the Standard Deviation of the list {2, 3, 4, 5, 6}?
(A) some value
(B) some value . ..
(E) some value "

The GMAT will not test your ability to calculate Standard Deviation. Instead, it'll test your understanding of the idea that Standard Deviation measures how spread out the data in a given set is.

So, the questions that you can get on Standard Deviation will be of the following types:

1.
Set P consists of 5 distinct integers. What is the standard deviation of set P?
(1) The mean of the set P is equal to the median of the set
(2) The 5 integers are consecutive

(Please note that since this is a DS question, you'll not be required to actually solve for the value of Standard Deviation. As you'll notice, this question is built upon the conceptual question posed by dabral in the post above)


2.
Which of the following sets will have the highest Standard Deviation?
For the following sets, which of the set would have the highest standard deviation
(A) {10, 20, 30}
(B) {99, 100, 101}
(C) {195, 200, 205}
(D) {992, 1000, 1008}
(E) {10001, 10002, 10003}



3.
For two sets P = {10, 20, 30} and Q= {15, 20, 25}, which of the following statements are true?
I. Standard Deviation(P) > Standard Deviation(Q)
II. If 5 is added to each term of set P, the standard deviation of set P will become equal to the standard deviation of Set Q
III. If each term of Set Q is multiplied by 2, the standard deviation of Set P will become equal to the standard deviation of Set Q.


Please also find below the links to a couple of Official questions on Standard Deviation:

http://gmatclub.com/forum/a-researcher-computed-the-mean-the-median-and-the-standard-134893.html
http://gmatclub.com/forum/list-m-not-shown-consists-of-8-different-integers-each-140777.html

For the GMAT, the concepts of Average (Mean) and Median are far more important and tested more frequently than the concept of Standard Deviation.

Hope this helped. :)

- Japinder
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
User avatar
Joined: 22 Apr 2015
Posts: 64
Re: Standard Deviation Formula  [#permalink]

Show Tags

New post 23 Apr 2015, 09:00
Hi AIMGMAT770,

Let's consider a series of n consecutive numbers: \(a, a+1, a+2......a+n-1\)
To find the standard deviation, we first calculate the mean, which in this case is same as the average of first and last number.
Mean = \((a+a+n-1)/2 = a + (n-1)/2\)

Next we need to find the squared distance of each number of the series from the mean:

Case 1: n is odd
For the 1st number, a -> \([a - (a + (n-1)/2)]^2 = [(n-1)/2]^2\)
For the 2nd number, a +1 -> \([a + 1 - (a + (n-1)/2)]^2 = [1-(n-1)/2]^2\)
.
.
.
For the number preceding the middle number, a + (n-1)/2 -1 -> \([a + (n-1)/2 -1- (a + (n-1)/2)]^2 = 1\)
For the middle number, a + (n-1)/2 (Mean is also the (n-1)/2th term of the series) -> \([a + (n-1)/2 - (a + (n-1)/2)]^2 = 0\)
For the number succeeding the middle number, a + (n-1)/2 + 1 ->\([a + (n-1)/2 +1- (a + (n-1)/2)]^2 = 1\)
.
.
.
For the second lat number, a +n -2 -> \([a + n -2 - (a + (n-1)/2)]^2 = [(n-1)/2-1]^2\)
For the last number, a +n -1 -> \([a + n -1 - (a + (n-1)/2)]^2 = [(n-1)/2]^2\)

Sum of the squared distance = \(2[1^2 + 2^2 + 3^2......[(n-1)/2]^2]\)
Variance = \(2[1^2 + 2^2 + 3^2......[(n-1)/2]^2]/n\)

Standard deviation = \(\sqrt{[2[1^2 + 2^2 + 3^2......[(n-1)/2]^2]/n]}\)

As sum of the squares of consecutive n numbers is n(n+1)(2n+1)/6

Hence, the Standard deviation simplifies to \(\sqrt{(n^2 -1)/12}\)

Case 2: n is even
For the 1st number, a -> \([a - (a + (n-1)/2)]^2 = [(n-1)/2]^2\)
For the 2nd number, a +1 -> \([a + 1 - (a + (n-1)/2)]^2 = [1-(n-1)/2]^2\)
.
.
.
For the number preceding the mean, a + (n-1)/2 - 0.5 -> \([a + (n-1)/2 -0.5 - (a + (n-1)/2)]^2 = 0.5^2\)
{a + (n-1)/2 (Mean is the average of the two middle terms and hence at a distance of 0.5 from them)}
For the number succeeding the mean, a + (n-1)/2 + 0.5 ->\([a + (n-1)/2 + 0.5 - (a + (n-1)/2)]^2 = 0.5^2\)
.
.
For the second last number, a +n -2 -> \([a + n -2 - (a + (n-1)/2)]^2 = [(n-1)/2-1]^2\)
For the last number, a +n -1 -> \([a + n -1 - (a + (n-1)/2)]^2 = [(n-1)/2]^2\)

Sum of the squared distance = \(2[0.5^2 + 1.5^2 + 2.5^2......[(n-1)/2]^2]\)
Variance = \(2[0.5^2 + 1.5^2 + 2.5^2......[(n-1)/2]^2]/n\)
Standard deviation = \(\sqrt{2[0.5^2 + 1.5^2 + 2.5^2......[(n-1)/2]^2]/n}\)

As you can see, in both the cases you only need to know the value of n to find the Standard deviation.

It is very unlikely that you will be asked to find the standard deviation but you can definitely get a DS question where the question stem asks you to find the standard deviation of a series of n consecutive numbers and one of the statements gives you the value of n.
All you need to understand here that if you know the number of terms, you can find the standard deviation.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8486
Premium Member
Re: Standard Deviation Formula  [#permalink]

Show Tags

New post 28 Jan 2018, 23:59
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

GMAT Club Bot
Re: Standard Deviation Formula &nbs [#permalink] 28 Jan 2018, 23:59
Display posts from previous: Sort by

Standard Deviation Formula

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.