1. **State the problem:** We have data on money spent on lottery tickets ranging from 1 to 1167. We want to group this data into 6 classes of equal width, starting with a lower limit of 1 for the first class and a class width of 200. 2. **Find class limits:** - The first class lower limit is 1. - Each class width is 200. - Class limits are intervals where each class covers 200 units. Calculate upper limits for each class: - Class 1: 1 to $1 + 200 - 1 = 200$ - Class 2: 201 to $201 + 200 - 1 = 400$ - Class 3: 401 to 600 - Class 4: 601 to 800 - Class 5: 801 to 1000 - Class 6: 1001 to 1200 (covers up to 1167) 3. **Class boundaries:** Class boundaries adjust class limits to avoid gaps between classes by subtracting 0.5 from lower limits and adding 0.5 to upper limits: - Class 1: 0.5 to 200.5 - Class 2: 200.5 to 400.5 - Class 3: 400.5 to 600.5 - Class 4: 600.5 to 800.5 - Class 5: 800.5 to 1000.5 - Class 6: 1000.5 to 1200.5 4. **Class midpoints:** Midpoint = $\frac{\text{lower boundary} + \text{upper boundary}}{2}$ - Class 1: $\frac{0.5 + 200.5}{2} = 100.5$ - Class 2: $\frac{200.5 + 400.5}{2} = 300.5$ - Class 3: $\frac{400.5 + 600.5}{2} = 500.5$ - Class 4: $\frac{600.5 + 800.5}{2} = 700.5$ - Class 5: $\frac{800.5 + 1000.5}{2} = 900.5$ - Class 6: $\frac{1000.5 + 1200.5}{2} = 1100.5$ **Final answers:** - Class limits: 1-200, 201-400, 401-600, 601-800, 801-1000, 1001-1200 - Class boundaries: 0.5-200.5, 200.5-400.5, 400.5-600.5, 600.5-800.5, 800.5-1000.5, 1000.5-1200.5 - Class midpoints: 100.5, 300.5, 500.5, 700.5, 900.5, 1100.5