Let's say I have a family and want to calculate the average consumed per person per day. I have two sets of measurements:
For the first 2 weeks, there are seven family members. For the next week, there are only six.
- Data Point 1: 235 lbs consumed over 14 days for all 7 people
- Data Point 2: 234 lbs consumed over 7 days for all 6 people
I want to know how much was consumer per person per day.
For a single data point, I can just use $c/a/d$. I could also use $c/d/a$, which gives the same result, but I'm not sure has the same meaning. More on this later.
With two data points, I need to use weighted averages, so something like $(c1/a1/d1 * d1 + c2/a2/d2 * d2)/(d1+d2)$. But I feel like I am weighting the days but not the people, but maybe that's already taken into account? I thought maybe a could double check the math by switching the divide order to $(c1/d1/a1 * a1 + c2/d2/a2 * a2)/(a1+a2)$, but I end up with a different result.
So either "consumed per person per day" is not equal to "consumed per day per person" or something is wrong with the math (maybe both). What is the correct calculation and explanation?