# Multi-variable weighted average

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?

• These numbers look odd. The first group suggests that each person ate about $2.4$ pounds of food a day. The second group suggests that each person ate $5.57$ . I understand it's the holiday season and all... – lulu Dec 16 '16 at 18:14
• The strangeness of the numbers aside, I assume that by "average" you mean the amount $x$ that has the property: "if every person consumed exactly $x$ per day, we'd get the same consumption as we actually got." Thus we'd have $14\times 7\times x + 7 \times 6 \times x = 235+234\implies 140x=469\implies x = 3.35$ .If you intended a different sort of average, you should clarify. – lulu Dec 16 '16 at 18:20