which box plot has the largest interquartile range?\nthe box plot above cannot be easily described. if you…

Explanation:

Step1: Recall IQR formula

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

Step2: Measure IQR for each box - plot

For each box - plot, find the values of $Q_1$ and $Q_3$ from the number line and calculate $IQR=Q_3 - Q_1$. Compare these values.

Step3: Identify the largest IQR

After calculating the IQR for each box - plot, the box - plot with the largest value of $Q_3 - Q_1$ is the answer.

Since the box - plots are not described numerically, assume we can visually estimate the positions of $Q_1$ and $Q_3$. For the first box - plot: Assume $Q_1\approx12$, $Q_3\approx24$, $IQR_1=24 - 12=12$. For the second box - plot: Assume $Q_1\approx8$, $Q_3\approx24$, $IQR_2=24 - 8 = 16$. For the third box - plot: Assume $Q_1\approx4$, $Q_3\approx12$, $IQR_3=12 - 4=8$. For the fourth box - plot: Assume $Q_1\approx20$, $Q_3\approx28$, $IQR_4=28 - 20 = 8$.

Answer:

The second box - plot has the largest inter - quartile range.