1. **State the problem:** We need to estimate the mean length from the grouped frequency table given. 2. **Identify the class intervals and frequencies:** - $0 < y \leq 5$, frequency $f_1 = 1$ - $5 < y \leq 10$, frequency $f_2 = 3$ - $10 < y \leq 15$, frequency $f_3 = 1$ 3. **Find the midpoints of each class interval:** - Midpoint $x_1 = \frac{0 + 5}{2} = 2.5$ - Midpoint $x_2 = \frac{5 + 10}{2} = 7.5$ - Midpoint $x_3 = \frac{10 + 15}{2} = 12.5$ 4. **Calculate the sum of frequency times midpoint:** $$\sum f_i x_i = (1)(2.5) + (3)(7.5) + (1)(12.5) = 2.5 + 22.5 + 12.5 = 37.5$$ 5. **Calculate the total frequency:** $$\sum f_i = 1 + 3 + 1 = 5$$ 6. **Calculate the mean:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i} = \frac{37.5}{5} = 7.5$$ 7. **Final answer:** The estimated mean length is $7.5$ cm (correct to 1 decimal place).