1. **State the problem:** We are given partial data about the number of medications senior citizens take, including frequencies, relative frequencies, and cumulative frequencies. We need to fill in the missing values in the table and find the percentage of seniors taking exactly zero medications. 2. **Given data and formulas:** - Frequency (f) is the count of seniors in each category. - Relative Frequency (rf) is calculated as $$\text{rf} = \frac{f}{\text{total}}$$ where total = 170. - Cumulative Frequency (cf) is the running total of frequencies up to that category. 3. **Calculate missing values for 2 medications:** - Frequency: $$f_2 = cf_2 - cf_1 = 109 - 73 = 36$$ - Relative Frequency: $$rf_2 = \frac{36}{170} = 0.2118$$ 4. **Calculate missing values for 3 medications:** - Frequency: $$f_3 = cf_3 - cf_2 = 137 - 109 = 28$$ - Relative Frequency: $$rf_3 = \frac{28}{170} = 0.1647$$ 5. **Completed table:** | # of medications | Frequency | Relative Frequency | Cumulative Frequency | |------------------|-----------|--------------------|----------------------| | 0 | 43 | 0.2529 | 43 | | 1 | 30 | 0.1765 | 73 | | 2 | 36 | 0.2118 | 109 | | 3 | 28 | 0.1647 | 137 | | 4 | 33 | 0.1941 | 170 | 6. **Calculate percentage of seniors taking exactly zero medications:** - Relative Frequency for 0 medications: 0.2529 - Percentage: $$0.2529 \times 100 = 25.29\%$$ **Final answers:** - a. Completed table as above. - b. Percentage taking zero medications = 25.29%