green valley middle school recorded the number of students in each homeroom. number of students 20 24 22 24…

Explanation:

Step1: Arrange data in ascending order

20, 22, 23, 24, 24, 24, 24, 26, 26, 26, 27, 28, 28, 28, 29, 30

Step2: Find the minimum value

The minimum value is 20.

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

There are 16 data points. The position of $Q_1$ is $\frac{16 + 1}{4}=4.25$. So, $Q_1$ is the value between the 4th and 5th ordered data points. $Q_1=\frac{24 + 24}{2}=24$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{16}{2}=8$ and $\frac{16}{2}+ 1 = 9$. So, $Q_2=\frac{26+26}{2}=26$.

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

The position of $Q_3$ is $3\times\frac{16 + 1}{4}=12.75$. So, $Q_3$ is the value between the 12th and 13th ordered data points. $Q_3=\frac{28+28}{2}=28$.

Step6: Find the maximum value

The maximum value is 30.

The box - plot should have a minimum value of 20, $Q_1 = 24$, median = 26, $Q_3=28$ and maximum value of 30.

Answer:

The box - plot with the minimum at 20, the left - hand side of the box at 24, the line in the box at 26, the right - hand side of the box at 28 and the maximum at 30. (The first box - plot shown in the image if we assume the order of presentation is from top to bottom).