Let's walk through the steps to find the first quartile (Q1), median (Q2), third quartile (Q3), and the maximum of the given data set.
1. List the Data Set:
The given data set is:
[tex]\[10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19\][/tex]
2. Sort the Data Set:
Sorting the data set from smallest to largest:
[tex]\[4, 10, 10, 11, 12, 12, 12, 12, 13, 13, 15, 15, 17, 18, 19, 20\][/tex]
3. Calculate the Quartiles and Maximum:
- First Quartile (Q1): This is the 25th percentile of the data set.
- Median (Q2): This is the 50th percentile, or the middle value, which divides the dataset into two equal halves.
- Third Quartile (Q3): This is the 75th percentile of the data set.
- Maximum Value: This is the highest value in the data set.
After performing the calculations for this sorted data set, we find:
- First Quartile (Q1): The value at the 25th percentile is [tex]\(11.75\)[/tex]
- Median (Q2): The value at the 50th percentile (middle value) is [tex]\(12.5\)[/tex]
- Third Quartile (Q3): The value at the 75th percentile is [tex]\(15.5\)[/tex]
- Maximum Value: The highest value in the set is [tex]\(20\)[/tex]
Given these calculations, the pairs are:
- First Quartile: [tex]\(11.75\)[/tex]
- Median: [tex]\(12.5\)[/tex]
- Third Quartile: [tex]\(15.5\)[/tex]
- Maximum: [tex]\(20\)[/tex]
So, the completed pairs are:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{first quartile} & \text{median} & \text{third quartile} & \text{maximum} \\
\hline
11.75 & 12.5 & 15.5 & 20 \\
\hline
\end{array}
\][/tex]
