[Math] How to calculate weighted average with a zero

average

I've got zero that needs to be weighted at 40%

I've then got a whole bunch of numbers let's say the average of 3,2,1,1,1 all weighted at 40%

I've then got another set of numbers, let's say the average of 2,1,1,1 weighted at 20%

Currently what I have is
( 0*.40 + AVG(3,2,1,1,1) *.40 + AVG(2,1,1,1) *0.2 ) / 100

But I guess what i'm trying to ask or figure out is, no matter what the weighting of 0 is, it will always be 0, which i'm not sure is correct or not. Can anyone provide any guidance?

Best Answer

You are finding the weighted average of three numbers, $a, b, c$, with weights 40%, 40%, 20% respectively. This is given by $$(0.4 \times a) + (0.4 \times b) + (0.2 \times c).$$

You are taking $a = 0$, $b= \frac{3+2+1+1+1}{5} = \frac{8}{5}$, $c= \frac{2+1+1+1}{4} = \frac{5}{4}$. So the weighted average is $$(0.4 \times 0) + (0.4 \times \frac{8}{5}) + (0.2 \times \frac{5}{4}) = 0.88.$$