1. **State the problem:** We are given a frequency distribution of players' speeds in km/hr and need to construct the relative frequency distribution. 2. **Formula for relative frequency:** $$\text{Relative Frequency} = \frac{\text{Frequency of class}}{\text{Total frequency}}$$ This tells us the proportion of the total players that fall into each speed interval. 3. **Calculate total frequency:** $$5 + 6 + 19 + 66 + 319 + 171 = 586$$ 4. **Calculate relative frequencies for each class:** - For 10–13.9 km/hr: $$\frac{5}{586} \approx 0.0085$$ - For 14–17.9 km/hr: $$\frac{6}{586} \approx 0.0102$$ - For 18–21.9 km/hr: $$\frac{19}{586} \approx 0.0324$$ - For 22–25.9 km/hr: $$\frac{66}{586} \approx 0.1126$$ - For 26–29.9 km/hr: $$\frac{319}{586} \approx 0.5444$$ - For 30–33.9 km/hr: $$\frac{171}{586} \approx 0.2918$$ 5. **Check sum of relative frequencies:** $$0.0085 + 0.0102 + 0.0324 + 0.1126 + 0.5444 + 0.2918 = 1.0000$$ This confirms our calculations are correct. **Final relative frequency distribution:** | Speed (km/hr) | Relative Frequency | |---------------|--------------------| | 10–13.9 | 0.0085 | | 14–17.9 | 0.0102 | | 18–21.9 | 0.0324 | | 22–25.9 | 0.1126 | | 26–29.9 | 0.5444 | | 30–33.9 | 0.2918 |