Answered

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Find the five-number summary for the following set of data.

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline Data & 4 & 7 & 9 & 9 & 13 & 13 & 17 & 19 & 21 & 23 \\
\hline
\end{tabular}

[tex]\[
\operatorname{Min} = \square
\][/tex]
[tex]\[
Q_1 = \square
\][/tex]
[tex]\[
Q_2 = \square
\][/tex]
[tex]\[
Q_3 = \square
\][/tex]
[tex]\[
\operatorname{Max} = \square
\][/tex]

Sagot :

GinnyAnswer
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]
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