17. Consider the data given below. \( 16,10,8,20,24,12,15,19,25 \) (i) Find the median of the data set. (ii) Find the inter quartile range of the data set.

**Step 1. Sort the Data** The given data set is: \[ 16,\ 10,\ 8,\ 20,\ 24,\ 12,\ 15,\ 19,\ 25 \] Sorting the data in ascending order, we have: \[ 8,\ 10,\ 12,\ 15,\ 16,\ 19,\ 20,\ 24,\ 25 \] **Step 2. Find the Median** Since there are \(9\) data points (an odd number), the median is the middle value. The middle element is the \(5^\text{th}\) value: \[ \text{Median} = 16 \] **Step 3. Find the Interquartile Range (IQR)** The interquartile range (IQR) is defined as: \[ \text{IQR} = Q_3 - Q_1 \] where \(Q_1\) is the first quartile (median of the lower half) and \(Q_3\) is the third quartile (median of the upper half). *Determine the Lower Half:* The lower half consists of the values below the median: \[ 8,\ 10,\ 12,\ 15 \] Since there are \(4\) values, the median of the lower half (i.e., \(Q_1\)) is the average of the middle two values: \[ Q_1 = \frac{10 + 12}{2} = \frac{22}{2} = 11 \] *Determine the Upper Half:* The upper half consists of the values above the median: \[ 19,\ 20,\ 24,\ 25 \] Similarly, the median of the upper half (i.e., \(Q_3\)) is the average of the middle two values: \[ Q_3 = \frac{20 + 24}{2} = \frac{44}{2} = 22 \] *Calculate the IQR:* \[ \text{IQR} = Q_3 - Q_1 = 22 - 11 = 11 \] **Final Answers:** - (i) The median of the data set is \(16\). - (ii) The interquartile range of the data set is \(11\).