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Thread: Mean averages question

  1. #1 Mean averages question 
    Forum Professor leohopkins's Avatar
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    What is the difference between a mean and a weighted mean ?

    Any help understanding this would be great


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I think the simple answer would be that the mean is a weighted mean with all the weights equal to 1, or 1/N depending on how the weights are defined.


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    Forum Professor leohopkins's Avatar
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    I thought you said that would be the simple answer :s

    I dont even know what "weighted mean" means but id like to know. Sorry I dont think my question was clear enough.
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    Forum Bachelors Degree Demen Tolden's Avatar
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    This is me trying to speak in set theory:

    I believe a weighted mean is a method that takes an average value of a data range where subsets of this data range are considered to have more significance than other subsets.

    Would someone describe this in set theory? I'd kind of like to see it.
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    Forum Professor leohopkins's Avatar
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    I can understand that. I wonder, where would the application of finding the weighted mean be useful ?
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  7. #6  
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    The Wikipedia article explains it.

    http://en.wikipedia.org/wiki/Weighted_mean
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    I just know the definition from statistics, pretty much what demen had said.

    its this expression for statistics

    where y is the random variable and P(y) is the probability at that value.
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    Quote Originally Posted by leohopkins
    I wonder, where would the application of finding the weighted mean be useful?
    Weighted means are used a lot in the statistics of the economy. For example, the Retail Price Index is a weighted mean; it is actually a weighted mean of weighted means but that is probably making things more complicated than required.

    A "weight" in this context can be taken to be a measure of relevance. Those items in your list that are more relevant have greater weight.

    There are also uses where the items with less relevance have greater weight. This method can be used to even out one of a number of characteristics effecting the values in your list allowing you to isolate the effect of some other characteristic. For example, electricity consumption in a household can vary with the time of day and with cost per unit; expensive electricity might be used more conservatively than cheaper electricity. So you could use weighted means to average out the effect of cost difference so that you can analyse the difference in useage purely by time of day.
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  10. #9  
    Forum Professor leohopkins's Avatar
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    I see, thankyou that makes perfect sense. So I would be right in saying that to find the weighted mean in say two different data sets; we would take the average mean within each data set, multiply it by the number of values and add it to the next data set calculation then finally divide the figure by the total number of values accross the whole range of data sets. ?

    Lets say if we had a million data sets, there would be no way of simplyfing this equation/calculation, would there ? Is that why the government needs super-computers to handle statistics ?
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    Quote Originally Posted by leohopkins
    ...we would take the average mean within each data set, multiply it by the number of values...
    No, that would not be right.

    Since: mean = (sum of values) / (number of values)

    then we have: (number of values) X mean = (sum of values)

    so you would have achieved very little.

    If you had a million sets you would first calculate the weighted mean of each set, giving you a further set, the set of weighted means. You would then calculate the weighted mean of the set of weighted means. (Or at least, that is one way of doing it).

    The actual mathematics involved is no more complicated than adding up numbers and dividing them by how many numbers there are, so simplifying this is not really necessary. The government needs large computers because the sets they deal with are both large and their values change frequently; the Retail Price Index is calculated every month. Computers also tend to do long, boring, repetitive tasks very accurately whilst humans make lots of mistakes.
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  12. #11  
    Forum Professor leohopkins's Avatar
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    Okay so lets say you had the following values:

    10, 20, 60, 80 and 80

    but the weight of the values in order are 10, 20, 20, 20, 30

    So then the weighted mean would be:

    (10x10)+(20x20)+(60x20)+(80x20)+(80x30) / 100 = 57

    The weighted mean would be 57

    Whereas, disregarding weights the mean average would be 50 ?

    So, if you have two seperate data sets:

    Data set 1) 10, 16, 33, 40, 61
    Data set 2) 5, 9, 12, 73

    The mean average of data set 1 is: 32
    The mean average of data set 2 is: 24.75

    32+24.25 / 2 = 28.375. So we could assume that the mean average accross the two data sets is 28.375. However, as far as I am aware this would be an incorrect assumption because the two data sets have different amount of values within them (one has 5 the other has 4)

    If we combined the two data sets together to form one data set and worked out the mean average from there, we would get 25.9, which differs from 28.375 by a margin of 2.475. (quite a lot)

    But if we know only the mean averages from my limited understanding we may do the following calculation:

    mean weighted average = (5)32+(4)24.75 / (4+5)
    This gives us the value: 28.777

    28.777 and 28.375 differ from each other slightly. Is this an acceptable calculation ?

    Also, how does one work out what 25.9 is of a proportion of 28.375 ? Is 28.375 - 25.9 / 100 correct as a calculation ?

    Thanks
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  13. #12  
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    Quote Originally Posted by leohopkins
    The weighted mean would be 57
    That is the correct method of calculation of the weighted mean, yes. But you can't just arrive at those weights randomly, they have to be obtained from somewhere. The usual method is to count the frequency with which that value occurs in your set.

    Quote Originally Posted by leohopkins
    The mean average of data set 1 is: 32
    We normally just say "the mean is 32". No one I've ever heard calls it the mean average; everyone knows the mean is an average and there is no need to state the obvious. The mean of set 1 is indeed 32, and the mean of set 2 is indeed 24.75, yes.

    Quote Originally Posted by leohopkins
    So we could assume that the mean average accross the two data sets is 28.375.
    That would depend on your purpose. If you want the average of all the values then you would add all the values together and divide by the number of values you have; in this case .........

    Quote Originally Posted by leohopkins
    But if we know only the mean averages ...we may do the following calculation: mean weighted average = (5)32+(4)24.75 / (4+5)
    This gives us the value: 28.777...
    That is not the weighted mean. That is the same figure I got for the mean of the complete set, above.

    Quote Originally Posted by leohopkins
    Is this an acceptable calculation ?
    Acceptable for what? The basic addition and division is correct, but you don't seem to have any understanding of: a) what you are trying to achieve, or b) what any of these numbers mean.

    I read on your website that you are going to University to study engineering. Can I suggest that you get yourself a more thorough grounding in basic mathematics and simple algebra before branching out on statistics (which is going to be of little use to you in engineering studies) and that you get your basic mathematics from something a little more rigorous than advice from some complete stranger on the web.

    Quote Originally Posted by leohopkins
    how does one work out what 25.9 is of [sic] a proportion of 28.375 ?
    The word proportion simply means "the quotient obtained by dividing a part by the whole" where, in this context, you can take quotient to be synonymous with a fraction. You want to know what A is as a proportion of B, then it is A/B. If you want to express this proportion as a percentage you multiply it by 100. So A as a percentage of B = (A/B) X 100.
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  14. #13  
    Forum Professor leohopkins's Avatar
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    Thanks for the advice. I have already started my Engineering degree and the mathematics module is all based on statistics; next year it will be moving on to geometry and quadratic algebra etc, etc. but for now I have to get to grips with it. True, I could easily email my tutor, but id rather email him and ask the same question on here because tutors are only human and can be wrong too : - )

    (And they seem to take longer to answer) :s

    One more thing........What is the point in using "sigma". I mean, why not just use brackets ?
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  15. #14  
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    Quote Originally Posted by leohopkins
    What is the point in using "sigma". I mean, why not just use brackets ?
    Mathematics is a language and its symbols are roughly synonymous with the words of any other language. So your question is more or less equivalent to asking: Road is such a weird word, why don't we just say week instead?

    You also need to bear in mind that mathematics is an international language, which means that in it you can speak to someone of whom you could not ask the time of day. Also, brackets are already used for a lot of other things. Sigma is just a letter of the Greek alphabet, before long all of its companions will be your friends too.
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  16. #15  
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    lol. okay thanks
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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