the data set represents the total number of pencils each student in a class needs to sharpen…

Explanation:

Step1: Arrange data in ascending order

$0,1,1,1,2,3,4,4,6,6,9$

Step2: Find the minimum value

The minimum value is $0$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 11$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{11+1}{4}=3$. So $Q_1 = 1$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{11 + 1}{2}=6$. So $Q_2=3$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$. So $Q_3 = 6$.

Step6: Find the maximum value

The maximum value is $9$.

A box - plot has a line at the minimum value ($0$), the left - hand side of the box at $Q_1(1)$, a line inside the box at the median ($3$), the right - hand side of the box at $Q_3(6)$ and a line at the maximum value ($9$).

Answer:

The box - plot that has a left - whisker starting at $0$, the left side of the box at $1$, the line inside the box at $3$, the right side of the box at $6$ and the right - whisker ending at $9$ is the correct one. Without specific labels for the given box - plots, based on the above analysis, you can identify the correct one among them.