Playbook
Averages
47 q · 9% HARD · about two a paper. Every question is a total divided by a count, or a weighted mean.
- Questions in the bank
- 47
- q/paper (21 papers)
- 2.24
- Tagged HARD
- 9%
- Subtopics
- 3
Strand: Quick-Win
When you’ll see it
A mean, a change in mean when someone joins or leaves, or groups combined.
How this chapter is tested
47 questions, about two a paper, at 9% HARD. Every question reduces to the total: mean × count.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Sum and mean
Total = mean × count; work with totals, not means.
Weighted averages
Combined mean = Σ nᵢ x̄ᵢ ÷ Σ nᵢ.
Consecutive numbers
The mean of an arithmetic run is its middle term.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Average of averages
Two class means are combined by class sizes, not averaged directly.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Averages notesDrill every Averages question
47 questions from the bank, across 3 subtopics.
Drill one subtopic at a time
The 3 subtopics, in teaching order.
- Sum and MeanDrill Sum and Mean
- Weighted and Combined AveragesDrill Weighted and Combined Averages
- Averages of Consecutive NumbersDrill Averages of Consecutive Numbers
Related playbooks
Often paired with this one — the technique or the trap overlaps. Drill these next.