To find the five-number summary for the given dataset:
[tex]\[ 4, 7, 9, 9, 13, 13, 17, 19, 21, 23 \][/tex]
Let's break it down step-by-step:
1. Minimum (Min): The smallest number in the dataset.
[tex]\[
\text{Min} = 4
\][/tex]
2. First Quartile (Q1): This represents the 25th percentile of the dataset.
[tex]\[
Q_1 = 9.0
\][/tex]
3. Median (Q2): The middle value of the dataset, also known as the 50th percentile.
[tex]\[
Q_2 = 13.0
\][/tex]
4. Third Quartile (Q3): This represents the 75th percentile of the dataset.
[tex]\[
Q_3 = 18.5
\][/tex]
5. Maximum (Max): The largest number in the dataset.
[tex]\[
\text{Max} = 23
\][/tex]
So, the five-number summary is:
[tex]\[
\begin{aligned}
\text{Min} &= 4 \\
Q_1 &= 9.0 \\
Q_2 &= 13.0 \\
Q_3 &= 18.5 \\
\text{Max} &= 23 \\
\end{aligned}
\][/tex]
Plugging these into the template:
[tex]\[
\operatorname{Min} = 4
\][/tex]
[tex]\[
Q_1 = 9.0
\][/tex]
[tex]\[
Q_2 = 13.0
\][/tex]
[tex]\[
Q_3 = 18.5
\][/tex]
[tex]\[
\text{Max} = 23
\][/tex]
