the data set represents the total number of pencils each student in a class needs to sharpen. 0, 1, 1, 1, 2…

Explanation:

Step1: Find the five - number summary

First, order the data set: $0,1,1,1,1,2,3,4,4,6,6,9$. The minimum value is $0$. The first quartile ($Q_1$): There are $n = 12$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{12+1}{4}=3.25$. So $Q_1$ is the value at the 3.25 - th position. Interpolating between the 3rd and 4th ordered values (both 1), $Q_1 = 1$. The median ($Q_2$): The position of the median is $\frac{n+1}{2}=\frac{12 + 1}{2}=6.5$. Interpolating between the 6th and 7th ordered values ($2$ and $3$), $Q_2=\frac{2 + 3}{2}=2.5$. The third quartile ($Q_3$): The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75$. Interpolating between the 9th and 10th ordered values ($4$ and $6$), $Q_3=\frac{4+6}{2}=5$. The maximum value is $9$.

Step2: Analyze box - plot features

The box in a box - plot has its left - hand side at $Q_1$, its right - hand side at $Q_3$, and a line inside the box at the median. The whiskers extend to the minimum and maximum values. The box should start at $1$, end at $5$, and have a line at $2.5$, with whiskers going to $0$ and $9$.

Answer:

Based on the above - calculated five - number summary, the box - plot with the box starting at 1, ending at 5, the line inside the box at 2.5, and whiskers going to 0 and 9 is the correct one (description of the correct box - plot among the given options, you need to visually check which one matches these criteria).