Use the data and your calculator to generate a modified boxplot. Identify the correct graph. \[ \begin{array}{llllllll}11 & 15 & 13 & 2 & 9 & 8 & 10 & 12\end{array} \]

To create a modified boxplot, we first need to calculate the five-number summary (minimum, first quartile \(Q_1\), median \(Q_2\), third quartile \(Q_3\), and maximum) and identify any outliers. ### Step 1: Sort the Data First, we sort the data in ascending order: \[ 2, 8, 9, 10, 11, 12, 13, 15 \] ### Step 2: Calculate the Five-Number Summary - **Minimum**: The smallest value is \(2\). - **Maximum**: The largest value is \(15\). - **Median (Q2)**: The median is the average of the two middle numbers (10 and 11): \[ Q_2 = \frac{10 + 11}{2} = 10.5 \] - **First Quartile (Q1)**: The first quartile is the median of the first half of the data (2, 8, 9, 10): \[ Q_1 = \frac{8 + 9}{2} = 8.5 \] - **Third Quartile (Q3)**: The third quartile is the median of the second half of the data (11, 12, 13, 15): \[ Q_3 = \frac{12 + 13}{2} = 12.5 \] ### Step 3: Calculate the Interquartile Range (IQR) The interquartile range is calculated as: \[ IQR = Q_3 - Q_1 = 12.5 - 8.5 = 4 \] ### Step 4: Determine Outliers Outliers are defined as any data points that fall below \(Q_1 - 1.5 \times IQR\) or above \(Q_3 + 1.5 \times IQR\). - Lower bound: \[ Q_1 - 1.5 \times IQR = 8.5 - 1.5 \times 4 = 8.5 - 6 = 2.5 \] - Upper bound: \[ Q_3 + 1.5 \times IQR = 12.5 + 1.5 \times 4 = 12.5 + 6 = 18.5 \] ### Step 5: Identify Outliers In this dataset, the only potential outlier is below the lower bound: - Values below \(2.5\): None - Values above \(18.5\): None Thus, there are no outliers in this dataset. ### Step 6: Create the Boxplot Now we can create the modified boxplot using the five-number summary: - Minimum: \(2\) - \(Q_1\): \(8.5\) - Median: \(10.5\) - \(Q_3\): \(12.5\) - Maximum: \(15\) ### Boxplot Representation The boxplot will have: - A box from \(Q_1\) (8.5) to \(Q_3\) (12.5) - A line at the median (10.5) - Whiskers extending from the minimum (2) to the maximum (15) ### Conclusion You can now draw the boxplot based on the calculated values. If you have options for the boxplot, look for one that matches the description above.