Weighted mean ( no idea where to start )

[James Smithson]

Just been given a question I have no idea where to start I have read all the information but I just do not understand. Going to need someone willing to put up with me for a bit and lots of silly questions to help me out here!!!

Here is the question....


(a) If you want to use the numbers of students as weights to calculate a weighted mean for the percentage of students studying for degree A what are the weights for Scotland 2015 and Wales 2015?

(b) The weights are quite different. How does this affect the overall weighted mean for the percentage of students studying for degree A?

(c) Use the numbers of students in each area in 2015 as weights to calculate the weighted mean for the percentage of students studyig degree A in 2015. Show your working.

The mean % of students studying for degree A in the dataset is 11.9. The weighted mean using the number of students in each of the combinations of area and year as weights, is 11.8. The total number of students in the dataset is 2842.


Okay that was the question. The info I have is as follows...

Area	Number	Degree B	Degree A
North West 2015	61	28%	11%
East 2015	90	26%	12%
Wales2015	42	33%	7%
Scotland 2015	164	18%	15%
Norhen Ireland 2015	40	35%	13%

I would rather work it out myself but I have now been at it 4 hours and done nothing getting very upset

thank you everyone in advance

James

 

[Dr.Peterson]

Just been given a question I have no idea where to start I have read all the information but I just do not understand. Going to need someone willing to put up with me for a bit and lots of silly questions to help me out here!!!

Here is the question....


(a) If you want to use the numbers of students as weights to calculate a weighted mean for the percentage of students studying for degree A what are the weights for Scotland 2015 and Wales 2015?

(b) The weights are quite different. How does this affect the overall weighted mean for the percentage of students studying for degree A?

(c) Use the numbers of students in each area in 2015 as weights to calculate the weighted mean for the percentage of students studyig degree A in 2015. Show your working.

The mean % of students studying for degree A in the dataset is 11.9. The weighted mean using the number of students in each of the combinations of area and year as weights, is 11.8. The total number of students in the dataset is 2842.


Okay that was the question. The info I have is as follows...

Area	Number	Degree B	Degree A
North West 2015	61	28%	11%
East 2015	90	26%	12%
Wales2015	42	33%	7%
Scotland 2015	164	18%	15%
Northern Ireland 2015	40	35%	13%

I would rather work it out myself but I have now been at it 4 hours and done nothing getting very upset

thank you everyone in advance

James

So, what did you do in those 4 hours? Please show us something. If it isn't calculations, maybe it's some thoughts about what the problem means, or some questions about why it says what it does. What does it mean to say the weights are the numbers of students? (Surely you can at least say what those numbers are.) What have you been taught about the effects of weighting on a mean?

 

[JeffM]

What purpose is served by taking a weighted mean of the different percentages? Why not just take the arithmetic mean?

Different question.

A weighted mean is a fraction. If we use the population of the regions as the weights, what does the denominator of the fraction represent?

 

[James Smithson]

So, what did you do in those 4 hours? Please show us something. If it isn't calculations, maybe it's some thoughts about what the problem means, or some questions about why it says what it does. What does it mean to say the weights are the numbers of students? (Surely you can at least say what those numbers are.) What have you been taught about the effects of weighting on a mean?

ok so the 4 hours is probably an exageration. I seriously dont unserstand what it wants is all.

I researched wieghted means and I understand ... not much actually ...

The wieghted mean of two or more numbers is :

sum of (number x wieght)
___________________________
Sum of wieghts


so if the wieght is the population of the region for example scotland is 164 and wales is 42

the sum of number ( im guessing is the total of 2842)

i think we have .... scotland ...


2842 x 164
____________ =2262.563107 ( i honestly dont know if this is right if it is I presume this is the wieght of scotland)
206



and wales ...


2842 x 42
____________ = 579.4368932
206

I wish I could understand it ... maybe its not 206 maybe its all the areas so its more like 397

making scotland 1174.025189
and wales 300.6649874


I will gladly put some more work in if I am going way of course and thank you both for replying !

 

[James Smithson]

42 x 11.8
_________ = 1.24836272 ( I dunno why but this pleases me more i feel like this is more likely to be correct)
397

 

[James Smithson]

Wait am I just been stupid surely a is just asking what the wieghts are so surely

scotland is 164 wales is 42 ....


not sure on b... maybe something like

A weighted mean always lies between the two numbers and it is nearer to the number that has the larger weight. Thus as Scotland has a larger weight than Wales the weighted mean will lay closer to Scotland.

and as for c not the foggiest..... at a guesss (61×11+90×12+42×7+164×15+40×13) / (61+90+42+164+40) = 12.65743073

 

[Dr.Peterson]

Wait am I just been stupid surely a is just asking what the wieghts are so surely

scotland is 164 wales is 42 ....

Yes, if you mean "the weights for Scotland 2015 and Wales 2015 are, respectively, 164 and 42."

not sure on b... maybe something like

A weighted mean always lies between the two numbers and it is nearer to the number that has the larger weight. Thus as Scotland has a larger weight than Wales the weighted mean will lay closer to Scotland.

Yes, if you mean "closer to the percentage for Scotland than to that for Wales." (The mean will not be somewhere in northern England!) But other numbers will also affect it, so I'd just say that Scotland's data has a larger effect than Wales'. But it's correct.

and as for c not the foggiest..... at a guesss (61×11+90×12+42×7+164×15+40×13) / (61+90+42+164+40) = 12.65743073

Correct.

What I'm not sure of is what role the last paragraph of the problem plays:

The mean % of students studying for degree A in the dataset is 11.9. The weighted mean using the number of students in each of the combinations of area and year as weights, is 11.8. The total number of students in the dataset is 2842.

 

[JeffM]

The sum of the weights that you are told to use is the number of students who were sampled in Great Britain as a whole, right?

When I multiply each weight (that is the number of students sampled in each region) by the percentage of sampled students taking course A in that region, what do I get?

So when all those products are added up, what does the result mean?

So what does the fraction mean?

 

[James Smithson]

thanks both for your help I am slowly working it out