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:

Answer:

First, we need to find the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum) of the data set: 5, 9, 7, 8, 7, 6, 8, 8, 5, 8, 5, 9, 10, 9, 6, 9.

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

The minimum value is 5.

Step3: Find the maximum

The maximum value is 10.

Step4: Find the median ($Q_2$)

There are $n = 16$ data points. The median is the average of the 8th and 9th ordered values. $\frac{8 + 8}{2}=8$.

Step5: Find the first quartile ($Q_1$)

The lower half of the data is 5, 5, 5, 6, 6, 7, 7, 8. There are 8 data points. The median of the lower half is the average of the 4th and 5th ordered values. $\frac{6+6}{2}=6$.

Step6: Find the third quartile ($Q_3$)

The upper half of the data is 8, 8, 9, 9, 9, 9, 10. There are 8 data points. The median of the upper half is the average of the 4th and 5th ordered values. $\frac{9 + 9}{2}=9$.

Based on the five - number summary (5, 6, 8, 9, 10), we can then determine which box - plot is correct (the box - plot with minimum at 5, $Q_1$ at 6, median at 8, $Q_3$ at 9, and maximum at 10). Without the actual options for box - plots labeled, we can't give a final choice among them, but the above are the steps to find the correct one. If we assume the box - plot with the correct minimum at 5, $Q_1$ at 6, median at 8, $Q_3$ at 9, and maximum at 10 is one of the choices, that would be the answer.