5. the data set represents the shoe sizes of 19 students in a fifth - grade physical education class. 4, 5…

Explanation:

Step1: Order the data

$4,5,5,5,6,6,6,6,7,7,7,7,7.5,7.5,8,8,8.5,8.5,9$ (already ordered)

Step2: Find the median (Q2)

There are $n = 19$ data - points. The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{19+1}{2}=10$ - th value. So, $Q2 = 7$.

Step3: Find the lower half of the data

The lower half consists of the first 9 values: $4,5,5,5,6,6,6,6,7$.

Step4: Find the median of the lower half (Q1)

There are 9 values. The median is the $\left(\frac{9 + 1}{2}\right)$-th value. $\frac{9+1}{2}=5$ - th value. So, $Q1 = 6$.

Step5: Find the upper half of the data

The upper half consists of the last 9 values: $7,7.5,7.5,8,8,8.5,8.5,9$.

Step6: Find the median of the upper half (Q3)

There are 9 values. The median is the $\left(\frac{9+1}{2}\right)$-th value. $\frac{9 + 1}{2}=5$ - th value. So, $Q3 = 8$.

Step7: Find the minimum and maximum

The minimum value is $4$ and the maximum value is $9$.

Step8: Draw the box - plot

1. Draw a number line that includes the range from $4$ to $9$.
2. Draw a box from $Q1 = 6$ to $Q3 = 8$.
3. Draw a vertical line inside the box at $Q2 = 7$.
4. Draw whiskers from the box to the minimum value ($4$) and the maximum value ($9$).

Answer:

A box - plot with a box from 6 to 8, a vertical line at 7 inside the box, and whiskers extending to 4 and 9 on the number line.