Relative Frequency 80B301
1. **Problem statement:** We need to find the percentage of cyclists younger than 18 surveyed between response 21 and response 40.
2. **Understanding relative frequency:** Relative frequency is the proportion of cyclists younger than 18 out of the total surveyed so far.
3. **Given data from the graph:**
- At 20 cyclists surveyed, relative frequency $f_{20} \approx 0.20$ (20%).
- At 40 cyclists surveyed, relative frequency $f_{40} \approx 0.30$ (30%).
4. **Calculate the number of cyclists younger than 18 at these points:**
- Number younger than 18 at 20 surveyed: $N_{20} = 20 \times 0.20 = 4$
- Number younger than 18 at 40 surveyed: $N_{40} = 40 \times 0.30 = 12$
5. **Find the number of cyclists younger than 18 surveyed between 21 and 40:**
$$N_{21-40} = N_{40} - N_{20} = 12 - 4 = 8$$
6. **Total cyclists surveyed between 21 and 40:**
$$40 - 20 = 20$$
7. **Calculate the percentage of cyclists younger than 18 in this interval:**
$$\text{Percentage} = \frac{N_{21-40}}{20} \times 100 = \frac{8}{20} \times 100 = 40\%$$
**Final answer:** 40% of the cyclists surveyed from response 21 to response 40 were younger than 18.