1. **State the problem:** We need to estimate the mean number of hours worked per week based on the given histogram data. 2. **Data from histogram:** - Intervals and frequencies: - 36-40 hours: 9 - 40-44 hours: 26 - 44-48 hours: 18 - 48-52 hours: 13 - 52-56 hours: 9 - 56-60 hours: 3 3. **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 interval. 4. **Calculate midpoints:** - 36-40: $\frac{36+40}{2} = 38$ - 40-44: $\frac{40+44}{2} = 42$ - 44-48: $\frac{44+48}{2} = 46$ - 48-52: $\frac{48+52}{2} = 50$ - 52-56: $\frac{52+56}{2} = 54$ - 56-60: $\frac{56+60}{2} = 58$ 5. **Calculate $f \times x$ for each interval:** - $9 \times 38 = 342$ - $26 \times 42 = 1092$ - $18 \times 46 = 828$ - $13 \times 50 = 650$ - $9 \times 54 = 486$ - $3 \times 58 = 174$ 6. **Sum frequencies and weighted values:** - $\sum f = 9 + 26 + 18 + 13 + 9 + 3 = 78$ - $\sum (f \times x) = 342 + 1092 + 828 + 650 + 486 + 174 = 3572$ 7. **Calculate mean:** $$\text{Mean} = \frac{3572}{78}$$ 8. **Simplify fraction:** $$\text{Mean} = \frac{\cancel{3572}}{\cancel{78}} = 45.7949$$ (rounded to 4 decimal places) 9. **Final answer rounded to one decimal place:** $$\boxed{45.8}$$ hours per week. This means the average number of hours worked per week by the respondents is approximately 45.8 hours.