1. **Problem statement:** We have a frequency distribution of hospitalization days and their frequencies. We need to find the mean (average) and the test score (assumed to be the mode here, as the problem options suggest). 2. **Given data:** - Days ($x$): 1, 2, 3, 4, 5 - Frequencies ($f$): 20, 10, 5, 10, 20 3. **Formula for the mean:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$ 4. **Calculate total frequency:** $$\sum f_i = 20 + 10 + 5 + 10 + 20 = 65$$ 5. **Calculate weighted sum:** $$\sum f_i x_i = (1 \times 20) + (2 \times 10) + (3 \times 5) + (4 \times 10) + (5 \times 20) = 20 + 20 + 15 + 40 + 100 = 195$$ 6. **Calculate mean:** $$\text{Mean} = \frac{195}{65} = 3$$ 7. **Determine the test score (mode):** The mode is the value with the highest frequency. Frequencies are 20, 10, 5, 10, 20. The highest frequency is 20, which occurs at days 1 and 5. Since the problem options suggest a single test score, and the options pair mean 3 with test score 3 or 5, the test score is likely 3 or 5. 8. **Check the median (middle value) as a possible test score:** Cumulative frequencies: - Up to day 1: 20 - Up to day 2: 30 - Up to day 3: 35 - Up to day 4: 45 - Up to day 5: 65 Median position: $\frac{65+1}{2} = 33$rd value, which lies in day 3 (since cumulative frequency up to day 2 is 30, and up to day 3 is 35). So median = 3. 9. **Conclusion:** Mean = 3, Test score (median) = 3. **Final answer:** א. 3; 3