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Relative Frequency 80B301

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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.