1. **State the problem:** We need to estimate the mean amount of money spent by 40 shoppers given grouped frequency data. 2. **Formula for mean from grouped data:** $$\text{Mean} = \frac{\sum (f \times x)}{\sum f}$$ where $f$ is the frequency and $x$ is the midpoint of each class interval. 3. **Calculate midpoints for each class interval:** - For $0 < a \leq 10$, midpoint $= \frac{0 + 10}{2} = 5$ - For $10 < a \leq 20$, midpoint $= \frac{10 + 20}{2} = 15$ - For $20 < a \leq 30$, midpoint $= \frac{20 + 30}{2} = 25$ - For $30 < a \leq 40$, midpoint $= \frac{30 + 40}{2} = 35$ - For $40 < a \leq 50$, midpoint $= \frac{40 + 50}{2} = 45$ 4. **Multiply each midpoint by its frequency:** - $5 \times 8 = 40$ - $15 \times 14 = 210$ - $25 \times 8 = 200$ - $35 \times 6 = 210$ - $45 \times 4 = 180$ 5. **Sum the products and frequencies:** - $\sum (f \times x) = 40 + 210 + 200 + 210 + 180 = 840$ - $\sum f = 8 + 14 + 8 + 6 + 4 = 40$ 6. **Calculate the mean:** $$\text{Mean} = \frac{840}{40}$$ 7. **Simplify the fraction:** $$\text{Mean} = \frac{\cancel{840}^{21}}{\cancel{40}^{1}} = 21$$ **Final answer:** The estimated mean amount of money spent by the 40 shoppers is **21**.