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

It is currently 25 Oct 2014, 16:47

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

How To Solve: Statistics

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
BSchool Thread Master
User avatar
Status: Tutor
Joined: 05 Apr 2011
Posts: 431
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 58

Kudos [?]: 255 [3] , given: 44

Premium Member
How To Solve: Statistics [#permalink] New post 13 Dec 2012, 07:15
3
This post received
KUDOS
3
This post was
BOOKMARKED
Hi All,

I have learned a lot from gmatclub and am done with my gmat too. So, i have decided to contribute back.
As part of this i have decided to share the knowledge i have regarding various topics related to gmat quant.
Hope it will be useful. This post is about how to solve "Statistics"

Theory

Mean (Arithmetic Mean) is the average of the all the numbers in the set.
Mean = (Sum of all the numbers in the set) / total number of numbers in the set

Suppose the set is {1,2,3,4,5}
Then, Mean = (1+2+3+4+5)/5 = 15 / 5 = 3

1. If all the numbers in the set are increased/decreased by the same number(k) then the mean also gets increased/decreased by the same number(k)

Suppose the set is {a,b,c,d,e}
then the Mean = (a+b+c+d+e)/5
Now, lets increase all the numbers by k. So, the new set is {a+k,b+k,c+k,d+k,e+k)
New Mean = (a+k +b+k +c+k +d+k + e+k)/5
= (a+b+c+d+e + 5k)/5 = ((a+b+c+d+e)/5 ) + k = Old Mean + k

2. If all the numbers in the set are multiplied/divided by the same number(k) then the mean also gets multiplied/divided by the same number(k)
Proof same as above. In this case if we multiple all the numbers by k then
New Mean = k* (Old Mean)

SUGGESTION: Don't try remembering the points 1 and 2 above. It does not take much time to calculate them!


Median is the middle value of the set.
In case of even number of numbers in the set: Median is the mean of the two middle numbers (after the numbers are arranged in the increasing / decreasing order)
Example: If the set is {5,1,4,6,3,2} then we will arrange the set as {1,2,3,4,5,6} and median will be mean of middle two terms. Middle two terms in this case are 3 and 4 so Median = (3+4)/2 = 3.5

In case of odd number of numbers in the set: Median is the middle number (after the numbers are arranged in increasing/ decreasing order )
Example: If the set is {4,5,3,1,2} then we will arrange the set as {1,2,3,4,5} and the median will be the middle number which is 3


1. If all the numbers in the set are increased/decreased by the same number(k) then the median also gets increased/decreased by the same number(k)
Proof same as for mean.

2. If all the numbers in the set are multiplied/divided by the same number(k) then the median also gets multiplied/divided by the same number(k)
Proof same as for mean.

3. In Case of evenly spaced set
Mean = Median = Middle term (if the number of terms is odd)
= Mean of middle terms (if the number of terms is even)

4. In case of consecutive integers: IF the number of integers is even then then the Mean = Median != Integer
Suppose the set is {1,2,3,4,5,6}
then Mean = Median = 3.5

SUGGESTION: Don't try remembering the points 1 and 2 above. It does not take much time to calculate them!


Range of a set is the difference between the highest and lowest value of the set.
Example: Suppose the set is {-1,2,3,6,8} then the range will be
8 -(-1) = 9

1. If all the numbers in the set are increased/decreased by the same number(k) then the range DOES NOT CHANGE!
Suppose the set is {a,b,c} (in increasing order)
Range = c-a
Now, lets increase all the numbers by k then the set will become {a+k, b+k, c+k}
New range = c+k -(a+k) = c-a = Old range

2. If all the numbers in the set are multiplied/divided by the same number(k) then the range also gets multiplied/divided by the same number(k)
Proof similar to that for mean.


Mode is the number which has occurred the maximum number of times in the set.
Suppose the set is {1,1,2,2,3,3,3,3,4,5}
then the mode is 3, as 3 has occurred the maximum number of times in the set.


Standard Deviation is an indicator of how spread the numbers are. Standard Deviation is the Root Mean Square (RMS) of the distance of the values from the mean.

Variance = (sum of (squares of difference of each number from mean )) / total number of numbers
Standard deviation = \sqrt{Variance}

Example:
Suppose the set is (1,2,3,4,5)
then Mean = 3
Variance = { (3-1)^2 + (3-2)^2 + (3-3)^2 + (3-4)^2 + (3-5)^2)} / 5
= (4+1+0+1+4)/5
= 2
Standard Deviation = \sqrt{Variance} = \sqrt{2}


Arithmetic Sequence is the sequence in which each number differs from its previous by a constant value (d)
Arithmetic sequence is generally denoted as
a , a+d , a+2d+,..., a+(n-1)d
where, a is the first term of the sequence.
d is the common difference
n is the number of terms in the sequence.
Tn is the nth term of the sequence.

Tn = a + (n-1)d
A.M. = Arithmetic mean of the sequence = Mean of First term and last term = (a + a+(n-1)d)/2
= (2a+ (n-1)d)/2
Sum of all the terms of the sequence = A.M. * n = (n/2) * (2a + (n-1)d)


Problems:

1. If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?

A. 395
B. 275
C. 355
D. 415
E. 365

Solution:
the mean of numbers 28, x, 42, 78 and 104 is 62
=> (28+x+42+78+104)/5 = 62
=> x = 58

the mean of 128, 255, 511, 1023 and x = mean of 128, 255, 511, 1023 and 58
= (128+255+511+1023+58)/5 = 1975/5 = 395

So, Answer will be A

link to the problem:
http://gmatclub.com/forum/if-the-mean-of-numbers-28-x-42-78-and-104-is-62-then-135288.html


2. Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three

Solution:
we need to first decide where will we position x
suppose we keep x at the center then the set in ascending order will be
{4,8,x,12,16}
now the median = x so the mean also has to be x
=> (4+8+x+12+16)/5 = x
=> x= 10
which is possible. So, x=10 is one such value

Now lets put x at the left of 8 so the median will be 8 now. So even the mean has to be 8
=> (4+8+x+12+16)/5 = 8
=> x= 0
Which is possible. So, x=0 is one such value

Now lets put x at the right of 12 so the median will be 12 now. So even the mean has to be 12
=> (4+8+x+12+16)/5 = 12
=> x= 20
Which is possible. So, x=20 is one such value

So, there are three such values for which mean = median.
So, answer will be D

link to the problem:
http://gmatclub.com/forum/set-s-consists-of-5-values-not-necessarily-in-ascending-144018.html


3. http://gmatclub.com/forum/set-a-3-3-3-4-5-5-5-has-a-standard-deviation-of-138266.html

Hope it helps!
Good Luck!
_________________

ankit
you must believe

How to start GMAT preparations?
How to Improve Quant Score?
gmatclub topic tags
Check out my GMAT debrief
Thursdays with Ron link
Looking for a Quant tutor? Check out my post for the same!

Combined Formula Sheet :
Number Properties || Word Problems and PnC || Equations, Inequalities || Geometry

How to Solve :
Statistics || Reflection of a line || Remainder Problems

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2871
Followers: 208

Kudos [?]: 43 [0], given: 0

Premium Member
Re: How To Solve: Statistics [#permalink] New post 05 Apr 2014, 22:25
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

Re: How To Solve: Statistics   [#permalink] 05 Apr 2014, 22:25
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic How to solve? n2739178 3 13 Mar 2011, 09:10
How to solve? SoniaSaini 3 25 Jan 2011, 20:37
How to solve ? samrand 1 15 Jan 2010, 05:14
SC- how to solve this? jennygmat 0 24 Mar 2005, 19:03
Display posts from previous: Sort by

How To Solve: Statistics

  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®.