Question: A swimming club has 200 members who are all either juniors or seniors.
114 of these members were juniors.
Of the juniors, 36 had won a trophy.
66 senior members had won a trophy.
Draw a frequency tree to represent this.
One member is chosen at random.
1. **State the problem:** We have a swimming club with 200 members divided into juniors and seniors.
2. **Given data:**
- Total members: $200$
- Juniors: $114$
- Juniors who won a trophy: $36$
- Seniors who won a trophy: $66$
3. **Calculate seniors:**
$$\text{Seniors} = 200 - 114 = 86$$
4. **Calculate juniors who did not win a trophy:**
$$114 - 36 = 78$$
5. **Calculate seniors who did not win a trophy:**
$$86 - 66 = 20$$
6. **Frequency tree structure:**
- Start with total $200$
- Split into juniors ($114$) and seniors ($86$)
- Juniors split into trophy winners ($36$) and non-winners ($78$)
- Seniors split into trophy winners ($66$) and non-winners ($20$)
7. **Interpretation:** This tree shows the distribution of members by category and trophy status.
Final answer: The frequency tree has branches:
- $200 \to 114$ juniors and $86$ seniors
- Juniors $114 \to 36$ trophy winners and $78$ non-winners
- Seniors $86 \to 66$ trophy winners and $20$ non-winners