1. **Problem Statement:** We have a frequency distribution of annual commission earnings (in thousands) for 150 salespeople. We want to find the proportion of salespeople earning less than $18,000. 2. **Understanding the Ogive:** An ogive is a cumulative frequency graph. To construct it, we calculate cumulative frequencies up to each class boundary. 3. **Data and Cumulative Frequencies:** - 0–5: 6 - 5–10: 12 - 10–15: 15 - 15–20: 35 - 20–25: 40 - 25–30: 23 - 30–35: 11 - 35–40: 8 Cumulative frequencies: - Up to 5: 6 - Up to 10: 6 + 12 = 18 - Up to 15: 18 + 15 = 33 - Up to 20: 33 + 35 = 68 - Up to 25: 68 + 40 = 108 - Up to 30: 108 + 23 = 131 - Up to 35: 131 + 11 = 142 - Up to 40: 142 + 8 = 150 4. **Find cumulative frequency at $18,000:** Since 18 lies between 15 and 20, we interpolate between cumulative frequencies at 15 and 20. Let $CF_{15} = 33$ and $CF_{20} = 68$. Interpolation formula: $$ CF_{18} = CF_{15} + \frac{18 - 15}{20 - 15} \times (CF_{20} - CF_{15}) $$ $$ CF_{18} = 33 + \frac{3}{5} \times (68 - 33) = 33 + 0.6 \times 35 = 33 + 21 = 54 $$ 5. **Calculate proportion:** Total salespeople = 150 Proportion earning less than $18,000: $$ \frac{54}{150} = 0.36 $$ **Final answer:** About 36% of the salespeople earn less than $18,000 annually.