1. **State the problem:** We are given grouped data with class intervals and their frequencies, and we need to find the mean of the data. 2. **Formula for mean of grouped data:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$ where $f_i$ is the frequency of the $i$th class and $x_i$ is the midpoint of the $i$th class. 3. **Calculate midpoints ($x_i$) for each class interval:** - For 30-34: $x_1 = \frac{30 + 34}{2} = 32$ - For 35-39: $x_2 = \frac{35 + 39}{2} = 37$ - For 40-44: $x_3 = \frac{40 + 44}{2} = 42$ - For 45-49: $x_4 = \frac{45 + 49}{2} = 47$ - For 50-54: $x_5 = \frac{50 + 54}{2} = 52$ - For 55-59: $x_6 = \frac{55 + 59}{2} = 57$ - For 60-64: $x_7 = \frac{60 + 64}{2} = 62$ - For 65-69: $x_8 = \frac{65 + 69}{2} = 67$ - For 70-74: $x_9 = \frac{70 + 74}{2} = 72$ 4. **Multiply each midpoint by its frequency ($f_i x_i$):** - $14 \times 32 = 448$ - $18 \times 37 = 666$ - $14 \times 42 = 588$ - $12 \times 47 = 564$ - $4 \times 52 = 208$ - $3 \times 57 = 171$ - $2 \times 62 = 124$ - $1 \times 67 = 67$ - $1 \times 72 = 72$ 5. **Sum of frequencies:** $$\sum f_i = 14 + 18 + 14 + 12 + 4 + 3 + 2 + 1 + 1 = 69$$ 6. **Sum of $f_i x_i$:** $$\sum f_i x_i = 448 + 666 + 588 + 564 + 208 + 171 + 124 + 67 + 72 = 2908$$ 7. **Calculate mean:** $$\text{Mean} = \frac{2908}{69}$$ 8. **Simplify fraction:** $$\text{Mean} = \frac{\cancel{2908}}{\cancel{69}} = 42.1$$ 9. **Final answer:** The mean of the grouped data is **42.1** (accurate to one decimal place).