Data Set: \( \begin{array}{llllllll}41 & 72 & 96 & 103 & 103 & 105 & 106 & 113\end{array} 118 \) Find the five number summary and IQR for the data set above. Leave answers as decimals if needed. Don't round. The minimum is

- The data set (in order) is: \(41,\; 72,\; 96,\; 103,\; 103,\; 105,\; 106,\; 113,\; 118\). - **Minimum:** The smallest number is the first element: \[ \text{Minimum} = 41 \] - **Median:** There are \(9\) data points. The median is the \(5^\text{th}\) value (since \(\frac{9+1}{2} = 5\)): \[ \text{Median} = 103 \] - **First Quartile (Q1):** Exclude the median and consider the lower half: \[ 41,\; 72,\; 96,\; 103 \] With \(4\) data points, Q1 is the average of the \(2^\text{nd}\) and \(3^\text{rd}\) values: \[ Q1 = \frac{72 + 96}{2} = \frac{168}{2} = 84 \] - **Third Quartile (Q3):** Exclude the median and consider the upper half: \[ 105,\; 106,\; 113,\; 118 \] With \(4\) data points, Q3 is the average of the \(2^\text{nd}\) and \(3^\text{rd}\) values: \[ Q3 = \frac{106 + 113}{2} = \frac{219}{2} = 109.5 \] - **Maximum:** The largest number is the last element: \[ \text{Maximum} = 118 \] - **Interquartile Range (IQR):** IQR is the difference between Q3 and Q1: \[ IQR = Q3 - Q1 = 109.5 - 84 = 25.5 \] Thus, the minimum is \(41\).