1. **Stating the problem:** We are given a frequency polygon representing heights of members in a netball club. Our task is to estimate the mean height to 1 decimal place. 2. **Identify the heights (midpoints) and their frequencies from the graph:** - Height (cm): 125, 150, 175, 200, 225 - Frequency: 9, 17, 18, 11, 8 3. **Calculate the weighted sum of heights multiplied by their frequencies:** $$ \text{Sum} = 125 \times 9 + 150 \times 17 + 175 \times 18 + 200 \times 11 + 225 \times 8 $$ Calculate each term: $$ 125 \times 9 = 1125 $$ $$ 150 \times 17 = 2550 $$ $$ 175 \times 18 = 3150 $$ $$ 200 \times 11 = 2200 $$ $$ 225 \times 8 = 1800 $$ 4. **Add them up:** $$ 1125 + 2550 + 3150 + 2200 + 1800 = 10825 $$ 5. **Calculate the total frequency:** $$ 9 + 17 + 18 + 11 + 8 = 63 $$ 6. **Calculate the mean height estimate:** $$ \text{Mean} = \frac{10825}{63} \approx 171.8254 $$ 7. **Round to 1 decimal place:** $$ 171.8 $$ **Final answer:** The estimated mean height is **171.8 cm**.