1. **Problem Statement:** We have a frequency distribution of annual commission earnings (in thousands) for 150 salespeople. We want to construct an ogive (cumulative frequency graph) and find the proportion of salespeople earning less than 18,000. 2. **Data given:** | Commission ($000) | Frequency | |-------------------|-----------| | 0–5 | 6 | | 5–10 | 12 | | 10–15 | 15 | | 15–20 | 35 | | 20–25 | 40 | | 25–30 | 23 | | 30–35 | 11 | | 35–40 | 8 | 3. **Step to construct ogive:** - Calculate cumulative frequencies by adding frequencies up to each class. 4. **Calculate cumulative frequencies:** - For 0–5: $6$ - For 5–10: $6 + 12 = 18$ - For 10–15: $18 + 15 = 33$ - For 15–20: $33 + 35 = 68$ - For 20–25: $68 + 40 = 108$ - For 25–30: $108 + 23 = 131$ - For 30–35: $131 + 11 = 142$ - For 35–40: $142 + 8 = 150$ 5. **Find cumulative frequency for $18,000$:** - Since $18$ lies in the class 15–20, use linear interpolation: - Class width = $20 - 15 = 5$ - Frequency in class = $35$ - Cumulative frequency before class = $33$ - Position of $18$ in class = $18 - 15 = 3$ - Interpolated cumulative frequency = $33 + \frac{3}{5} \times 35 = 33 + 21 = 54$ 6. **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.