I ran a survey on my website where users marked a checkbox for what % they did X. Something like this.
How much of your shopping do you do online?
[] 0%
[] 25%
[] 50%
[] 75%
[] 100%
For the results I got the following.
0% -- 3%
25% -- 35%
50% -- 44%
75% -- 17%
100% -- 2%
What I am trying to determine is what percentage does the average respondent spend online.
Best Answer
The quantity you seek is a weighted average:
$$\begin{align} \mathrm{mean\_percentage} &= \frac{(0 \% \cdot 0.03) + (25 \% \cdot 0.35) + (50 \% \cdot 0.44) + (75 \% \cdot 0.17) + (100 \% \cdot 0.02) }{0.03 + 0.35 + 0.44 + 0.17 + 0.02}\\ &\approx 45.9 \% \end{align}$$
Two things should be noted here: 1) I wrote the computation of the average this way because I wanted to illustrate the role of the data (the percent spent on line) against the weights (what fraction selected a particular data point), which in this case may have been a little confusing; 2) your weights did not quite add to $1$, but rather $1.01$, which is OK given rounding error, but still, you should always put the sum of the weights in the denominator to keep the computation accurate.