1. **Stating the problem:** We have two tables: one with counts of students in sports and chess club categories, and another with relative frequencies (percentages). We need to fill in the missing percentages in the second table based on the counts from the first table. 2. **Understanding the data:** From the first table (counts): - In sports program and in chess club: 45 - Not in sports program and in chess club: 60 - Total in chess club: 105 - In sports program and not in chess club: 80 - Not in sports program and not in chess club: 65 - Total not in chess club: 145 - Total in sports program: 125 - Total not in sports program: 125 - Grand total: 250 3. **Formula for relative frequency:** $$\text{Relative frequency} = \frac{\text{Count}}{\text{Total number of students}} \times 100\%$$ 4. **Calculate missing percentages:** - Percentage in sports program and in chess club: $$\frac{45}{250} \times 100 = 18\%$$ (given) - Percentage not in sports program and in chess club: $$\frac{60}{250} \times 100 = 24\%$$ (given) - Total percentage in chess club: $$\frac{105}{250} \times 100 = 42\%$$ (missing, calculate) - Percentage in sports program and not in chess club: $$\frac{80}{250} \times 100 = 32\%$$ (given) - Percentage not in sports program and not in chess club: $$\frac{65}{250} \times 100 = 26\%$$ (missing, calculate) - Total percentage not in chess club: $$\frac{145}{250} \times 100 = 58\%$$ (given) - Total percentage in sports program: $$\frac{125}{250} \times 100 = 50\%$$ (given) - Total percentage not in sports program: $$\frac{125}{250} \times 100 = 50\%$$ (given) - Grand total percentage: $$\frac{250}{250} \times 100 = 100\%$$ (given) 5. **Summary of missing values:** - Total percentage in chess club: 42% - Percentage not in sports program and not in chess club: 26% 6. **Explanation:** We use the counts divided by the total number of students (250) and multiply by 100 to get the percentages. The missing percentages are found by applying this formula to the respective counts. **Final answer:** - Total percentage in chess club: 42% - Percentage not in sports program and not in chess club: 26%