# Math Help - Weighted Probability

1. ## 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?]

2. Originally Posted by ragnar
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

3. 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.

4. Originally Posted by ragnar
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