The cue is overlapping groups in a mean question: some people's ratings are included in both group averages. Multiply each mean by its group size in Desmos to recover the rating totals, then subtract the shared group's total once. Divide by the count of distinct people, not the sum of the group counts. Remove the overlap from both the rating total and the headcount.
Hints
- Hint 1
A mean is a group's rating total divided by its size. Work backward by multiplying each activity's average by its volunteer count. What rating total did the volunteers in both activities contribute?
- Hint 2
The overlap is the volunteers in both groups. Adding the two activity totals counts each shared volunteer's one rating twice. What must you subtract so the total counts each volunteer's rating once?
Step-by-step
Recover the totals and remove the overlap
Step 1Find each group's rating total
A mean is a group's rating total divided by its volunteer count, so multiply each mean by its count to recover the three rating totals. Type , , and in Desmos. It shows for gardening, for tutoring, and for the volunteers in both.
- Step 2
Count the shared ratings only once
Each volunteer gave exactly one rating, but the overlap, the volunteers in both activities, is included in both activity totals. Adding those totals counts their twice. Subtract it once, so each rating contributes once: . Type in Desmos. It shows .
- Step 3
Divide by the distinct volunteer count
The corrected total belongs to the distinct volunteers, not to separate people. To find their mean, divide that total by their count. Type in Desmos; it shows . The mean feedback rating is . Grid in 69.