1. **Problem Statement:** We have petrol usage data (in litres) for 40 boda boda riders and the cost per litre is 160. 2. **Step (a): Frequency Distribution Table** - Class size = 0.5, starting at 1.5 litres. - Classes: 1.5-1.99, 2.0-2.49, 2.5-2.99, 3.0-3.49, 3.5-3.99, 4.0-4.49 - Count data points in each class: - 1.5-1.99: 1.7,1.6,1.8,1.9,1.8,1.5,1.5 → 7 - 2.0-2.49: 2.1,2.1,2.4,2.1,2.3,2.4,2.0,2.3 → 8 - 2.5-2.99: 2.8,2.8,2.5,2.6,2.9,2.9,2.9,2.6,2.7,2.7,2.8,2.7 → 12 - 3.0-3.49: 3.1,3.1,3.2,3.3,3.4,3.4,3.4,3.5,3.1 → 9 - 3.5-3.99: 3.6,3.7,3.9 → 3 - 4.0-4.49: 4.0,4.1,4.3 → 3 | Class Interval | Frequency | |---------------|-----------| | 1.5 - 1.99 | 7 | | 2.0 - 2.49 | 8 | | 2.5 - 2.99 | 12 | | 3.0 - 3.49 | 9 | | 3.5 - 3.99 | 3 | | 4.0 - 4.49 | 3 | 3. **Step (b)(i): Estimate Mean Amount Spent** - Midpoints: 1.75, 2.25, 2.75, 3.25, 3.75, 4.25 - Multiply midpoints by frequencies: - $1.75 \times 7 = 12.25$ - $2.25 \times 8 = 18$ - $2.75 \times 12 = 33$ - $3.25 \times 9 = 29.25$ - $3.75 \times 3 = 11.25$ - $4.25 \times 3 = 12.75$ - Sum of products = $12.25 + 18 + 33 + 29.25 + 11.25 + 12.75 = 116.5$ - Mean litres = $\frac{116.5}{40} = 2.9125$ - Mean cost = $2.9125 \times 160 = 466$ (rounded to nearest integer) 4. **Step (b)(ii): Estimate Median Amount Spent** - Total frequency = 40, median position = $\frac{40}{2} = 20^{th}$ value - Cumulative frequencies: - 1.5-1.99: 7 - 2.0-2.49: 7 + 8 = 15 - 2.5-2.99: 15 + 12 = 27 - Median class is 2.5-2.99 (since 20th value lies here) - Median formula: $$\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f}\right) \times c$$ where - $L = 2.5$ (lower boundary of median class) - $N = 40$ - $F = 15$ (cumulative frequency before median class) - $f = 12$ (frequency of median class) - $c = 0.5$ (class width) $$\text{Median} = 2.5 + \left(\frac{20 - 15}{12}\right) \times 0.5 = 2.5 + \frac{5}{12} \times 0.5 = 2.5 + 0.2083 = 2.7083$$ - Median cost = $2.7083 \times 160 = 433.33$ **Final answers:** - (a) Frequency distribution table as above. - (b)(i) Mean amount spent = 466 - (b)(ii) Median amount spent = 433.33