which box plot has an iqr of 10?

Explanation:

Step1: Recall IQR formula

The inter - quartile range (IQR) is calculated as $IQR = Q_3 - Q_1$, where $Q_3$ is the third - quartile and $Q_1$ is the first - quartile. In a box - plot, the left edge of the box is $Q_1$ and the right edge of the box is $Q_3$.

Step2: Check each box - plot

For the first box - plot: Assume the left edge of the box ($Q_1$) is at 3 and the right edge of the box ($Q_3$) is at 13. Then $IQR=13 - 3=10$. For the second box - plot: If we assume the left edge of the box ($Q_1$) is at 1 and the right edge of the box ($Q_3$) is at 11, $IQR = 11-1 = 10$. But we need to check others too. For the third box - plot: Assume the left edge of the box ($Q_1$) is at 7 and the right edge of the box ($Q_3$) is at 11, then $IQR=11 - 7 = 4$. For the fourth box - plot: Assume the left edge of the box ($Q_1$) is at 5 and the right edge of the box ($Q_3$) is at 9, then $IQR=9 - 5 = 4$.

Answer:

The first box - plot (where the left edge of the box is at 3 and the right edge is at 13) has an IQR of 10.