1. **State the problem:** We have a sample survey with categories A, B, and C. We need to prepare a frequency distribution table, calculate relative frequencies and percentages, find the percentage of category B, and draw a bar graph. 2. **Frequency distribution table:** Count the occurrences of each category: - A: 7 times - B: 7 times - C: 11 times 3. **Calculate relative frequencies and percentages:** Total number of elements $= 7 + 7 + 11 = 25$ Relative frequency for each category is given by: $$\text{Relative frequency} = \frac{\text{Frequency}}{\text{Total number of elements}}$$ - For A: $$\frac{7}{25} = 0.28$$ - For B: $$\frac{7}{25} = 0.28$$ - For C: $$\frac{11}{25} = 0.44$$ Percentages are relative frequencies multiplied by 100: - For A: $0.28 \times 100 = 28\%$ - For B: $0.28 \times 100 = 28\%$ - For C: $0.44 \times 100 = 44\%$ 4. **Percentage of elements in category B:** From above, category B percentage is $28\%$. 5. **Bar graph description:** - Bar for A at height 7 - Bar for B at height 7 - Bar for C at height 11 This matches the frequency distribution.