Certainly! Let's go through the steps to complete the task and display the data set using a box plot.
### Step-by-Step Solution:
1. Arrange the numbers in order from lowest to highest:
Given data set: [tex]\[2, 3, 5, 6, 8, 9, 12\][/tex]
These numbers are already in ascending order.
2. Identify the maximum value in the data set:
The maximum value in the ordered data set is [tex]\(12\)[/tex].
Having completed these steps, we now have the ordered data set and the maximum value.
### Visualizing with a Box Plot:
A box plot, also known as a whisker plot, can be created using the ordered data. This plot visually shows the distribution and spread of the data through its quartiles.
To create a box plot, you need the following five-number summary:
- Minimum value
- First quartile (Q1)
- Median (Q2)
- Third quartile (Q3)
- Maximum value
For our data set [tex]\([2, 3, 5, 6, 8, 9, 12]\)[/tex]:
- Minimum value: [tex]\(2\)[/tex]
- First quartile (Q1): Value separating the lowest 25% of the data. For our set, Q1 is the average of the second and third values: [tex]\( \frac{3 + 5}{2} = 4\)[/tex].
- Median (Q2): Middle value: [tex]\(6\)[/tex]
- Third quartile (Q3): Value separating the highest 25% of the data. For our set, Q3 is the average of the fifth and sixth values: [tex]\( \frac{8 + 9}{2} = 8.5\)[/tex].
- Maximum value: [tex]\(12\)[/tex]
With this five-number summary, we can proceed to draw the box plot:
```
______|_______
____|______|______|_______|______|____________________________
2 3 4 6 8.5 9 12
```
In this box plot:
- The horizontal line represents the minimum and maximum values.
- The edges of the box represent the first quartile (Q1) and the third quartile (Q3).
- The line inside the box represents the median (Q2).
These elements give a clear visualization of the spread and central tendency of the data set.
