Som grae, 12.7 Calouate quarties and intergarcle range voy In the data set below, what is the interquartile range \[ \begin{array}{llllll}20 & 32 & 60 & 65 & 71 & 71 \\ 81 & 92\end{array} \]

To calculate the **interquartile range (IQR)** for the given data set, follow these steps: **Given Data Set:** \[ 20, \ 32, \ 60, \ 65, \ 71, \ 71, \ 81, \ 92 \] **Step 1: Order the Data** The data is already ordered from smallest to largest. **Step 2: Find the Median (Q2)** Since there are 8 data points (an even number), the median is the average of the 4th and 5th values. \[ \text{Median (Q2)} = \frac{65 + 71}{2} = \frac{136}{2} = 68 \] **Step 3: Find the First Quartile (Q1)** Q1 is the median of the first half of the data (the lower 50%). First half: \[ 20, \ 32, \ 60, \ 65 \] \[ Q1 = \frac{32 + 60}{2} = \frac{92}{2} = 46 \] **Step 4: Find the Third Quartile (Q3)** Q3 is the median of the second half of the data (the upper 50%). Second half: \[ 71, \ 71, \ 81, \ 92 \] \[ Q3 = \frac{71 + 81}{2} = \frac{152}{2} = 76 \] **Step 5: Calculate the Interquartile Range (IQR)** \[ \text{IQR} = Q3 - Q1 = 76 - 46 = 30 \] **Conclusion:** The **interquartile range (IQR)** of the given data set is **30**.