Sixth grade \( \quad 31.7 \) Calculate quartiles and interquartile range MNV In the data set below, what is the interquartile range? \( \begin{array}{lllllll}3 & 1 & 8 & 9 & 6 & 1\end{array} \) Submit

To find the **interquartile range (IQR)** of the given data set, follow these steps: ### **Step 1: Organize the Data in Ascending Order** Start by arranging the numbers from smallest to largest. Original data: 3, 1, 8, 9, 6, 1 Sorted data: **1, 1, 3, 6, 8, 9** ### **Step 2: Determine the Quartiles** - **Number of Data Points (n):** 6 Since the number of data points is even, we'll split the data into two halves: - **Lower Half:** 1, 1, 3 - **Upper Half:** 6, 8, 9 **First Quartile (Q₁):** This is the median of the lower half. - For the lower half (1, 1, 3), the median is **1**. **Third Quartile (Q₃):** This is the median of the upper half. - For the upper half (6, 8, 9), the median is **8**. ### **Step 3: Calculate the Interquartile Range (IQR)** \[ \text{IQR} = Q₃ - Q₁ \] \[ \text{IQR} = 8 - 1 = 7 \] ### **Conclusion** The **interquartile range** of the data set is **7**.