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#1 2013-04-06 05:38:06

clueless101
Member
Registered: 2013-04-06
Posts: 5

Weighted averages

How would you find the weighted average of example 14 different countries with different unemployment rates?

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#2 2013-04-06 05:41:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Weighted averages

Hi;

Weighted really just means multiplying the data by constants. What are you taking an average of? Do you have some data?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-04-06 05:42:48

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,621
Website

Re: Weighted averages

Weighted Average of the countries = ((Frequency 1)*(Rate 1) + (Frequency 2)*(Rate 2) + ...)/14

Maybe I need to know more about the problem


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2013-04-06 05:53:21

clueless101
Member
Registered: 2013-04-06
Posts: 5

Re: Weighted averages

Hey there
The  unemployment rate of the 14 countries are the following:

4.0
7.2
6.8
6.6
8.3
7.8
7.8
9.6
6.7
5.1
3.9
7.8
7.8
14.8

Weighted Average is 8.2%
How did they get this 8.2??

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#5 2013-04-06 05:56:23

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,621
Website

Re: Weighted averages

just add 'em up and divide by 14


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2013-04-06 06:09:32

clueless101
Member
Registered: 2013-04-06
Posts: 5

Re: Weighted averages

I have been trying that, but not getting to 8.2

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#7 2013-04-06 06:10:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Weighted averages

I do not think you are providing everything. Where are the weights?

You will need them to get 8.2


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2013-04-06 06:15:33

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Weighted averages

Hi clueless101,

There must be another column for weights, by default we take weight to be 1 for each country.

We get 104.2 / 14 = 7.44285714286


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#9 2013-04-06 06:23:34

clueless101
Member
Registered: 2013-04-06
Posts: 5

Re: Weighted averages

The book only gives me the country names and the unemployment rates

btw thanks guys for your time

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#10 2013-04-06 06:25:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Weighted averages

Hi;

That is the entire question? You are sure you have not left anything out?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2013-04-06 06:38:51

clueless101
Member
Registered: 2013-04-06
Posts: 5

Re: Weighted averages

They do mention that the weights are necessary since the populations of the countries are different. If they were all equal the average would be the sum of all percentages divided by 14.

other than that it's just the country names which I left out

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#12 2013-04-06 06:40:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Weighted averages

Maybe they want you to look up the populations of the countries.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#13 2013-04-06 06:44:57

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,376

Re: Weighted averages

Yes that's the weight that is needed.

If you weren't given them, you'll have to look them up.

simple example to show why you have to do this.

Suppose country A has 1000 people and 100 are unemployed.  That's 10% unemployed.

Suppose country B has 10 people and 9 are unemployed.  That's 90% unemployed.

If you just do (10 + 90)/2 = 50, you've given too much importance to country B

You need to go back to the raw data.

Total population = 1000 + 10 = 1010
Total unemployed = 109.

So true average = 109/1010 x 100 = 10.8%

The answer is properly weighted towards the larger population.

Using the formula {(1000 x 10) + (10 x 90)} / 1010 = 10.8

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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