Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 02:35

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

Mergin sets and arithmetic mean

Author Message
TAGS:

Hide Tags

Director
Joined: 23 Apr 2010
Posts: 581
Followers: 2

Kudos [?]: 86 [0], given: 7

Mergin sets and arithmetic mean [#permalink]

Show Tags

30 Nov 2011, 07:51
Say that we have two sets S and T that we merge to form a single set V. What is the relation between the sum of averages of S and T and an average of V if we know that the sets contain only positive numbers?

I think that it is: AVG(S) + AVG(T) > AVG(V)

Thanks.
Manager
Joined: 09 Nov 2011
Posts: 128
Followers: 1

Kudos [?]: 58 [0], given: 16

Re: Mergin sets and arithmetic mean [#permalink]

Show Tags

30 Nov 2011, 07:56
I think the relation would be Avg (S) + Avg(T) < Avg(V)...
_________________

Time to play the game...

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1180
Followers: 438

Kudos [?]: 1603 [0], given: 4

Re: Mergin sets and arithmetic mean [#permalink]

Show Tags

30 Nov 2011, 12:04
nonameee wrote:
Say that we have two sets S and T that we merge to form a single set V. What is the relation between the sum of averages of S and T and an average of V if we know that the sets contain only positive numbers?

I think that it is: AVG(S) + AVG(T) > AVG(V)

If both averages are positive, then yes, your inequality will be true. But we can say a lot more. The situation you're describing is that of a conventional weighted average. We have two groups, each with their own average. When we combine the two groups, the combined average must be *in the middle* of the two group averages. So if you know, say, that AVG(S) < AVG(T), then you could be certain that:

AVG(S) < AVG(V) < AVG(T)

The larger set T is relative to set S (in ratio terms), the closer the average of V will be to the average of T.

You encounter this situation in word problems very frequently. If, say, at a company, women earn on average $44/hour, and men earn on average$36/hour, then the average wage for all employees certainly must be somewhere between $36 and$44. The higher the proportion of employees who are women, the closer the average will be to \$44.

Finally in this example, it certainly is true that the combined average is less than the sum of 36 and 44, but that doesn't really give you especially useful information.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Director
Joined: 23 Apr 2010
Posts: 581
Followers: 2

Kudos [?]: 86 [0], given: 7

Re: Mergin sets and arithmetic mean [#permalink]

Show Tags

30 Nov 2011, 15:22

The reason I asked this question is because it appeared in one of the GmatClub tests (Test24):

Quote:
21. If sets S and T are merged into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

(1) S and T are one-element sets
(2) Neither set S nor set T contains negative numbers

So, I wanted to study the properties of averages when combining sets containing various numbers (positive, negative, same numbers etc.). If we allow numbers to be negative, I found no straightforward rule as the one I mentioned in my first post.
Re: Mergin sets and arithmetic mean   [#permalink] 30 Nov 2011, 15:22
Similar topics Replies Last post
Similar
Topics:
A good source for Statistics (Arithmetic Mean, Mode, Median) 5 24 May 2015, 21:49
Averages (Arithmetic Means) 0 04 Nov 2014, 09:39
When median = mean, is the set always evenly spaced? 2 18 Nov 2013, 21:23
Will standard deviation and mean uniquely identify a set? 7 29 Jan 2012, 07:36
1 In a set of consecutive ODD integers, the mean ALWAYS equals 6 01 Apr 2015, 20:21
Display posts from previous: Sort by