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Math Help - Weighted Probability

  1. #1
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    Weighted Probability

    So I'm reading through this text on stats and it uses the example where, in some town, the percentage of 1-person households is 12, 2-person households is 30, 3-person households is 23, and 4-person + is 65. Now it says that, to find the average we take (1*12 + 2*30 + 3*23 + 7*65)/100 = 6-ish, guessing that 7-person households is a good guess for a decent representative number of all households that are 4-person +. My question is, is the proper way to understand this as: For any given household, it's size is about 6. However I would need to do something slightly different if I wanted to know, for any given person what is the size of his household--right?--wrong?

    [Edit: I'm starting to think this should be the other way around, because we multiply 2 by its percentage to represent each person in the household, so this weighted average would represent, for any given person, his household is about 6. So if I wanted each household to count just once, then I would have to do something different. Perhaps take the average of the percentages, (12+30+23+65)/4 = 32-ish, and so the typical percentage in the chart is 32, and so this will represent where the typical household is in the ordering, and since 32>30 then the typical household is just a little bigger than a 2-person household? Right? Wrong?]
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ragnar View Post
    So I'm reading through this text on stats and it uses the example where, in some town, the percentage of 1-person households is 12, 2-person households is 30, 3-person households is 23, and 4-person + is 65. Now it says that, to find the average we take (1*12 + 2*30 + 3*23 + 7*65)/100 = 6-ish, guessing that 7-person households is a good guess for a decent representative number of all households that are 4-person +. My question is, is the proper way to understand this as: For any given household, it's size is about 6. However I would need to do something slightly different if I wanted to know, for any given person what is the size of his household--right?--wrong?
    Without a reason to suppose that the average size of a household given it has 4 or more members is 7 is pure nonsense (and the information needed to justify this is exactly what has been thrown out by the binning).

    Worse yet the percentages add to more than 100!

    CB
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    I'm not sure what binning is. But yeah, the last percentage should be 45, my bad. Anyway, supposedly the reason for choosing 7 is just common sense that the amount of 8- and 9- and 10-person households are very very small in comparison to the rest, and those which are 10+ are probably negligible, so 7 is an informed guess.

    Anyway, the thing I'm most interested in is the precise interpretation of the numbers being used. We can, if desired for simplicity, say that there are only 1-, 2-, 3-, and 4-person households and do the numbers in the obvious way, but I want to check that the resulting weighted average represents something like the typical household rather than the household of the typical person.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ragnar View Post
    I'm not sure what binning is. But yeah, the last percentage should be 45, my bad. Anyway, supposedly the reason for choosing 7 is just common sense that the amount of 8- and 9- and 10-person households are very very small in comparison to the rest, and those which are 10+ are probably negligible, so 7 is an informed guess.

    Anyway, the thing I'm most interested in is the precise interpretation of the numbers being used. We can, if desired for simplicity, say that there are only 1-, 2-, 3-, and 4-person households and do the numbers in the obvious way, but I want to check that the resulting weighted average represents something like the typical household rather than the household of the typical person.
    It would be the average household size.

    CB
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