Question

mrs. clark, a gym teacher, recorded the number of laps each student ran around the gym in ten minutes. laps run: 5 9 7 8 7 6 8 8 5 8 5 9 10 9 6 9 which box plot represents the data?

Explanation:

Step1: Arrange data in ascending order

5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10

Step2: Find the minimum value

The minimum value is 5.

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

There are 16 data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{16+ 1}{4}=4.25$. So, $Q_1=\frac{6 + 6}{2}=6$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{16 + 1}{2}=8.5$. So, $Q_2=\frac{8+8}{2}=8$.

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

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(16 + 1)}{4}=12.75$. So, $Q_3=\frac{9+9}{2}=9$.

Step6: Find the maximum value

The maximum value is 10.

Answer:

The box - plot with minimum at 5, $Q_1$ at 6, median at 8, $Q_3$ at 9 and maximum at 10 represents the data. Without seeing the full set of box - plot options, we can say that the box - plot should have the box start at 6, end at 9, have a line inside the box at 8 and whiskers extending to 5 and 10.