1. The problem involves calculating the mean ($\bar{x}$) from grouped frequency data. 2. The formula for the mean of grouped data is: $$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$ where $f_i$ is the frequency of the $i$th class and $x_i$ is the midpoint of the $i$th class interval. 3. From the table, the class intervals and frequencies ($f$) are: - 8-18 with $f=4$ - 12-17 with $f=8$ - 18-29 with $f=10$ 4. Calculate the midpoints ($x_i$) of each class: - For 8-18: $x_1 = \frac{8+18}{2} = 13$ - For 12-17: $x_2 = \frac{12+17}{2} = 14.5$ - For 18-29: $x_3 = \frac{18+29}{2} = 23.5$ 5. Multiply each midpoint by its frequency: - $4 \times 13 = 52$ - $8 \times 14.5 = 116$ - $10 \times 23.5 = 235$ 6. Sum the products and frequencies: - $\sum f_i x_i = 52 + 116 + 235 = 403$ - $\sum f_i = 4 + 8 + 10 = 22$ 7. Calculate the mean: $$\bar{x} = \frac{403}{22} \approx 18.32$$ Therefore, the mean $\bar{x}$ is approximately 18.32.