Let's analyze the provided dataset step-by-step and fill in the missing information for the box plot.
The given data set is:
[tex]\[ 2, 3, 5, 6, 8, 9, 12. \][/tex]
### Step-by-Step Solution
1. Arrange the numbers in order:
The data is already ordered from lowest to highest:
[tex]\[ 2, 3, 5, 6, 8, 9, 12. \][/tex]
2. Identify the minimum value:
The minimum value of the dataset is:
[tex]\[ 2. \][/tex]
3. Identify the maximum value:
The maximum value of the dataset is:
[tex]\[ 12. \][/tex]
4. Calculate the median:
For a dataset of 7 numbers, the median is the middle number (4th number in the ordered list):
[tex]\[ \text{Median} = 6. \][/tex]
5. Calculate the lower quartile (Q1):
The lower quartile (Q1) is the median of the lower half of the dataset. The lower half of the dataset (excluding the median) is:
[tex]\[ 2, 3, 5. \][/tex]
The median of this subset is the middle number:
[tex]\[ Q1 = 3. \][/tex]
To summarize, the analysis provides the following:
- Minimum value: [tex]\( 2 \)[/tex]
- Maximum value: [tex]\( 12 \)[/tex]
- Median (Q2): [tex]\( 6 \)[/tex]
- Lower quartile (Q1): [tex]\( 3 \)[/tex]
Therefore, for the given box plot:
- The minimum value is [tex]\( 2 \)[/tex] [tex]\(\checkmark\)[/tex].
- The maximum value is [tex]\( 12 \)[/tex] [tex]\(\checkmark\)[/tex].
- The median of the data (Q2) is [tex]\( 6 \)[/tex] [tex]\(\checkmark\)[/tex].
- The lower quartile (Q1) is [tex]\( 3 \)[/tex] [tex]\(\square\)[/tex].
