1. **State the problem:** We need to estimate the mean daily energy output from a histogram showing frequency density versus energy output intervals. 2. **Recall the formula for mean from a histogram:** $$\text{Mean} = \frac{\sum (\text{midpoint} \times \text{frequency})}{\sum \text{frequency}}$$ 3. **Calculate frequencies:** Frequency for each bar is given by frequency density \( \times \) class width. 4. **Calculate midpoints and frequencies for each interval:** - Interval 0 to 3 kWh: midpoint = $\frac{0+3}{2} = 1.5$, frequency density = 1, width = 3, frequency = $1 \times 3 = 3$ - Interval 3 to 5 kWh: midpoint = $\frac{3+5}{2} = 4$, frequency density = 3, width = 2, frequency = $3 \times 2 = 6$ - Interval 5 to 6 kWh: midpoint = $\frac{5+6}{2} = 5.5$, frequency density = 4, width = 1, frequency = $4 \times 1 = 4$ - Interval 6 to 8 kWh: midpoint = $\frac{6+8}{2} = 7$, frequency density = 1, width = 2, frequency = $1 \times 2 = 2$ 5. **Calculate numerator (sum of midpoint times frequency):** $$3 \times 1.5 + 6 \times 4 + 4 \times 5.5 + 2 \times 7 = 4.5 + 24 + 22 + 14 = 64.5$$ 6. **Calculate denominator (sum of frequencies):** $$3 + 6 + 4 + 2 = 15$$ 7. **Calculate mean:** $$\text{Mean} = \frac{64.5}{15} = 4.3$$ **Final answer:** The estimated mean daily energy output is **4.3 kWh** (to 1 decimal place).