1) Find the interquartile range of this data set; \[ 12.10,16,10,5,11,11,12,10,12,9 \]

To find the **interquartile range (IQR)** of the data set: \[ 12.10, 16, 10, 5, 11, 11, 12, 10, 12, 9 \] Follow these steps: ### 1. **Sort the Data:** First, arrange the data in ascending order. \[ 5, 9, 10, 10, 11, 11, 12, 12, 12.10, 16 \] ### 2. **Determine the Quartiles:** Since there are **10 data points** (an even number), we'll split the data into two halves to find the first quartile (Q₁) and the third quartile (Q₃). - **Lower Half:** The first 5 numbers. \[ 5, 9, 10, 10, 11 \] - **Q₁ (First Quartile):** The median of the lower half. \[ Q₁ = 10 \] - **Upper Half:** The last 5 numbers. \[ 11, 12, 12, 12.10, 16 \] - **Q₃ (Third Quartile):** The median of the upper half. \[ Q₃ = 12 \] ### 3. **Calculate the Interquartile Range (IQR):** \[ \text{IQR} = Q₃ - Q₁ = 12 - 10 = 2 \] ### **Answer:** The interquartile range of the data set is **2**.