GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 11 Jul 2020, 06:54

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

Theory issue regarding averages

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

Hide Tags

Theory   
Find Similar Topics 
Manager
Manager
avatar
B
Joined: 16 Jul 2018
Posts: 102
GMAT ToolKit User Premium Member CAT Tests
Theory issue regarding averages  [#permalink]

Show Tags

New post 28 May 2020, 04:06
Hello guys,
I have a query regarding averages so I will try to ask the question by providing some examples to make myself clear.
Let's say that we have 2 sets A and B and we want to find the average of both those sets.
set A (1,3,8) set B (1,2,3)
Average of A=4
Average of B= 2
Average of both sets (4+2)/2=3

Alternatively (1+3+8+1+2+3)/6=3
As we can see in both cases the average is the same


However there are cases in which the above 2 approaches have 2 different results

set A ( 1,5,7,9) set B(13,14)
Average of set A= 5.5
Average of set B= 13.5
Average of set A and B= 19/2= 9.5

Alternatively (1+5+7+9+13+14)/6=8.16

Could someone shed some light on the issue that I have?
GMAT Tutor
User avatar
G
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 642
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Theory issue regarding averages  [#permalink]

Show Tags

New post 29 May 2020, 02:49
1
Top Contributor
Average of two sets = Sum of all the numbers in both the sets/Total Number of numbers in both the sets

Example 1:
In this case you have the same number of elements in both the sets (3 each)
So when you are trying to do (Average of A + Average of B)/2 then it is still equal to average of both the sets because
((Average of A)*3 + (Average of B)*3) / 6 will give you the same result.
So, if you have same number of elements in two or more sets and if you want to take the average of all the sets together then you can still take the average of individual sets and then take average of all the sets to get average of all the sets together.

Example 2:
In this case you have different number of elements in both the sets (First has 4 and other has 2)
If you want to use the averages calculated for individual sets then you can do the following:
(4 *(Average of A) + 2*(Average of B)) / 6
But if you notice then 4*Average of A is same as Sum of all elements of A. SO, you can directly do some of all the elements in both the sets / total number of elements in both the sets.

When we find averages of two or more sets then you can also think about it as weighted average, instead of thinking of it as just average. Here weight is nothing but the total number of elements.
Hope it helps!


In Example 1
UNSTOPPABLE12 wrote:
Hello guys,
I have a query regarding averages so I will try to ask the question by providing some examples to make myself clear.
Let's say that we have 2 sets A and B and we want to find the average of both those sets.
set A (1,3,8) set B (1,2,3)
Average of A=4
Average of B= 2
Average of both sets (4+2)/2=3

Alternatively (1+3+8+1+2+3)/6=3
As we can see in both cases the average is the same


However there are cases in which the above 2 approaches have 2 different results

set A ( 1,5,7,9) set B(13,14)
Average of set A= 5.5
Average of set B= 13.5
Average of set A and B= 19/2= 9.5

Alternatively (1+5+7+9+13+14)/6=8.16

Could someone shed some light on the issue that I have?

_________________
GMAT Tutor
avatar
P
Joined: 24 Jun 2008
Posts: 2308
Re: Theory issue regarding averages  [#permalink]

Show Tags

New post 29 May 2020, 03:10
1
If you're combining two sets, and finding the average of the combined set, then you're always calculating what is known as a "weighted average". The average is "weighted" by the sizes of the sets (by the ratio of their sizes, technically). So if one set is twice as big as the other, the average you calculate will be "twice as close" to the bigger set's average -- the bigger set is twice as important as the smaller one.

So if you wanted to find the average income for people in the USA and in Canada, then since the USA has about ten times as many people as Canada, the USA's average is going to be far more important than Canada's average. You could not just find the USA average, and the Canada average, and then average those two numbers. You'd need to do a weighted average calculation. Weighted averages are too big a topic to get into in a short post, but one way to get the right answer is to give the USA average a weight of 10 (i.e. multiply it by 10) and the Canada average a weight of 1, and then divide by 10 + 1 = 11. So if average income in the US is $31,000 and in Canada is $20,000, then the overall average will be

[(10)(31,000) + (1)(20,000)] / 11 = 30,000

If you look at how far the answer here is from the individual averages, you'll notice it's 10 times as far from Canada's average than from the USA average. In non-grammatical speak, you could say the answer is "10 times as close" to the USA average (that's not correct English though). That's identical to the ratio of the sizes of the two populations, and weighted averages always work out that way. That observation is the basis for a different weighted average method that is sometimes called "alligation", which you could look into, though that method takes a bit of practice. If you can learn it though, it's the best weighted average method for GMAT purposes.
_________________
GMAT Tutor in Montreal

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
Manager
Manager
avatar
B
Joined: 16 Jul 2018
Posts: 102
GMAT ToolKit User Premium Member CAT Tests
Re: Theory issue regarding averages  [#permalink]

Show Tags

New post 29 May 2020, 03:14
BrushMyQuant IanStewart thank you both for the prompt response and the detailed explanations.
GMAT Club Bot
Re: Theory issue regarding averages   [#permalink] 29 May 2020, 03:14

Theory issue regarding averages

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne