Question

Following is a list of the number of hazardous waste sites in states in a recent year. The list has been sorted into numerical order. Construct a boxplot for these data. The median is 20, Qv1 is 14, and Qv3 is 34 .

0
1
3
4
4
5
7
8
8
8
9
9
14
15
15
15
16
16
16
16
18
18
18
19
20
20
21
22
23
23
24
25
26
28
29
30
32
34
36
40
41
43
44
45
54
71
79
95
97
110

Answer 1

To construct a boxplot, we first need to determine the key components: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values. Based on the data provided and the summary statistics you gave:

- **Minimum (Min)**: The smallest value in the dataset is **0**.
- **First Quartile (Q1)**: This is given as **14**.
- **Median (Q2)**: This is given as **20**.
- **Third Quartile (Q3)**: This is given as **34**.
- **Maximum (Max)**: The largest value in the dataset is **110**.

Now we can summarize these values:

- Minimum: 0
- Q1 (First Quartile): 14
- Median (Q2): 20
- Q3 (Third Quartile): 34
- Maximum: 110

### Boxplot Construction Steps:
1. **Draw a number line** that includes the range from the minimum (0) to the maximum (110).
2. **Draw a box** from Q1 (14) to Q3 (34). This represents the interquartile range (IQR).
3. **Draw a line** inside the box at the median (20).
4. **Extend "whiskers"** from the sides of the box:
- The left whisker extends to the minimum (0).
- The right whisker extends to the maximum (110).
5. **Optional**: If there are any outliers, they should be plotted as individual points beyond the whiskers, but in this case, since the maximum is much larger than Q3, it might be considered an outlier. However, for the sake of the boxplot, we just include it in the whisker.

### Boxplot Representation:
```
|----|-----|---------------|-----------------|--------------|--------|
0 14 20 34 110
Q1 Median Q3
```
In a graphical boxplot:
- The box spans from Q1 (14) to Q3 (34).
- The line at 20 represents the median (Q2).
- A whisker extends from 14 to 0, and another whisker extends from 34 to 110.

With these steps, you can now visualize the boxplot representation of your dataset!