Question

question #2 the shoe sizes for members of the track team at a high school are shown in the set below. {7, 7 1/2, 8, 8, 8 1/2, 9, 10, 10 1/2, 10 1/2, 11 1/2, 11 1/2, 13, 14} which box - and - whisker plot best represents the data set?

Explanation:

Step1: Arrange data in order

$7,7\frac{1}{2},8,8,8\frac{1}{2},9,10,10\frac{1}{2},10\frac{1}{2},11\frac{1}{2},11\frac{1}{2},13,14$

Step2: Find the minimum

The minimum value is $7$.

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

There are $n = 13$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{13+ 1}{4}=3.5$. So, $Q_1=\frac{8 + 8}{2}=8$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{13+1}{2}=7$. So, $Q_2 = 10$.

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

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(13 + 1)}{4}=10.5$. So, $Q_3=\frac{11\frac{1}{2}+11\frac{1}{2}}{2}=11\frac{1}{2}$.

Step6: Find the maximum

The maximum value is $14$.

Answer:

We need to match these values (minimum = 7, $Q_1$ = 8, $Q_2$ = 10, $Q_3$ = 11.5, maximum = 14) to the box - and - whisker plots. Without seeing the visual details of the plots to choose from, we have calculated the key values for the correct box - and - whisker plot representation. If you can describe the plots further in terms of the positions of the minimum, $Q_1$, $Q_2$, $Q_3$ and maximum on them, we can determine the correct one. But the calculated values for the box - and - whisker plot are: minimum = 7, $Q_1$ = 8, median ($Q_2$)=10, $Q_3$ = 11.5, maximum = 14.