1. **Problem Statement:** Given the GPA data of 15 students: 3.4, 3.9, 4.0, 2.8, 3.5, 2.6, 3.2, 3.6, 1.9, 2.1, 2.0, 3.3, 2.4, 1.8, 3.2, find the range, interquartile range (IQR), and number of outliers. 2. **Step 1: Sort the data in ascending order:** $$1.8, 1.9, 2.0, 2.1, 2.4, 2.6, 2.8, 3.2, 3.2, 3.3, 3.4, 3.5, 3.6, 3.9, 4.0$$ 3. **Step 2: Find the range:** The range is the difference between the maximum and minimum values. $$\text{Range} = 4.0 - 1.8 = 2.2$$ 4. **Step 3: Find the interquartile range (IQR):** Given from the problem, the first quartile $Q_1 = 2.1$ and the third quartile $Q_3 = 3.5$. $$\text{IQR} = Q_3 - Q_1 = 3.5 - 2.1 = 1.4$$ 5. **Step 4: Find outliers using the 1.5*IQR rule:** Calculate the lower and upper bounds: $$\text{Lower bound} = Q_1 - 1.5 \times IQR = 2.1 - 1.5 \times 1.4 = 2.1 - 2.1 = 0$$ $$\text{Upper bound} = Q_3 + 1.5 \times IQR = 3.5 + 1.5 \times 1.4 = 3.5 + 2.1 = 5.6$$ 6. **Step 5: Identify outliers:** Any data point below 0 or above 5.6 is an outlier. Since all data points are between 1.8 and 4.0, there are no outliers. **Final answers:** - Range: $2.2$ - Interquartile Range (IQR): $1.4$ - Number of outliers: $0$