A mean is the total divided by the number of values. If every value increases by the same amount, the mean increases by that amount too, so you don't need the individual values. Read “more pages” as adding, not multiplying, and don't leave the mean unchanged.
Hints
- Hint 1
The mean is a fair-share value: imagine sharing the total pages equally among the students. If every student reads more pages, what happens to that fair share?
- Hint 2
Adding the same amount to each student's page count also adds that amount to the mean. Start with the mean given for this week; what one operation gives next week's mean?
Step-by-step
Shift the mean
Step 1Translate the change in pages
No Desmos needed. The given mean and the change for every student determine the new mean directly. Let be one student's page count this week. “ more pages” means add , not multiply by :
- Step 2
Apply the change to the mean
The mean is the total divided by the number of students. Every student's count goes up by , while the number of students stays the same, so the fair-share count goes up by too. Adding the same amount to every value adds that amount to the mean. Apply this to the given mean:
- Step 3
Find next week's mean
Add the increase:
So the mean next week is pages. Choice C.