# Weighted average of household size given number of households of each size

I hope this isn't too simple to bother you with, but this calculation is at the center of a dispute at work and I want to make sure I'm on solid ground here.

To begin with, we know that the average household size of a particular jurisdiction in 2010 was 3.26 members per household.

However, we also have the following breakdown of households by size:

1,280 one-person households

3,236 two-person households

3,770 three-person households

3,200 four-person households

2,106 five-person households

2,443 households with six members or more.

Based on these figures, and assuming for the sake of argument that there are no households with more than six members, I calculate a weighted average household size of around 3.56. Furthermore, given that there probably are households with more than six members, I would say that the average could not possibly be lower than 3.56--certainly not as low as 3.26.

$$\frac{1 \times 1280 + 2 \times 3236 + 3 \times 3770 + 4 \times 3200 + 5 \times 2106 +6 \times 2443}{1280+3236+3770+3200+2106+2443}= \frac{57050}{16035}= 3.56$$