1. **Stating the problem:** We are given a histogram with bars representing frequency density over intervals of height (m). We want to find the total frequency (number of observations) represented by the histogram. 2. **Formula used:** The total frequency is the sum of the areas of the bars in the histogram. Each bar's area = width of the interval $ \times $ frequency density (height). 3. **Calculate each bar's area:** - Bar 1: Interval 0-10, width = 10, height = 1 $$\text{Area}_1 = 10 \times 1 = 10$$ - Bar 2: Interval 10-15, width = 5, height = 5 $$\text{Area}_2 = 5 \times 5 = 25$$ - Bar 3: Interval 15-20, width = 5, height = 1.5 $$\text{Area}_3 = 5 \times 1.5 = 7.5$$ - Bar 4: Interval 20-40, width = 20, height = 0.5 $$\text{Area}_4 = 20 \times 0.5 = 10$$ - Bar 5: Interval 40-50, width = 10, height = 0.5 $$\text{Area}_5 = 10 \times 0.5 = 5$$ 4. **Sum all areas to find total frequency:** $$\text{Total frequency} = 10 + 25 + 7.5 + 10 + 5 = 57.5$$ 5. **Interpretation:** The total frequency represented by the histogram is 57.5, which should be close to the total number of observations (houses) counted. Since frequency must be a whole number, this suggests either rounding in the histogram or data. **Final answer:** $$\boxed{57.5}$$