1. **State the problem:** We are given the admission prices for 10 theme parks: 55, 65, 40, 40, 30, 50, 64, 45, 40, 41. We need to find the **range** and the **interquartile range (IQR)** of this data set. 2. **Formulas and definitions:** - The **range** is the difference between the maximum and minimum values in the data set. - The **interquartile range (IQR)** is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$), i.e., $$\text{IQR} = Q_3 - Q_1$$ 3. **Step 1: Order the data from smallest to largest:** $$30, 40, 40, 40, 41, 45, 50, 55, 64, 65$$ 4. **Step 2: Calculate the range:** - Maximum value = 65 - Minimum value = 30 - Range = $$65 - 30 = 35$$ 5. **Step 3: Find the quartiles:** - Since there are 10 data points, the median is the average of the 5th and 6th values: $$\text{Median} = \frac{41 + 45}{2} = \frac{86}{2} = 43$$ - The lower half (first 5 values): $$30, 40, 40, 40, 41$$ - $Q_1$ is the median of the lower half, which is the 3rd value: $$Q_1 = 40$$ - The upper half (last 5 values): $$45, 50, 55, 64, 65$$ - $Q_3$ is the median of the upper half, which is the 3rd value: $$Q_3 = 55$$ 6. **Step 4: Calculate the interquartile range:** $$\text{IQR} = Q_3 - Q_1 = 55 - 40 = 15$$ **Final answers:** - Range = 35 - Interquartile Range = 15