Statistics, STD2 EQ-Bank 03 MC

For the data below, which is the correct five figure summary?

\(12,\ \ 16, \ \ 4,\ \ 6, \ \ 4, \ \ 5, \ \ 22, \ \ 20, \ \ 12, \ 8\ \)

\(4,\ \ 5, \ \ 8,\ \ 16, \ \ 21\)
\(4,\ \ 5, \ \ 8,\ \ 16, \ \ 22\)
\(4,\ \ 5, \ \ 10,\ \ 16, \ \ 21\)
\(4,\ \ 5, \ \ 10,\ \ 16, \ \ 22\)

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\(D\)

Show Worked Solution

\(\text{Ordered data set}\ \rightarrow\ \ 4,\ \ 4, \ \ 5,\ \ 6, \ \ 8, \ \ 12, \ \ 12, \ \ 16, \ \ 20, \ 22\ \)

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} & 4\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} & \dfrac{8+12}{2}=10\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} & 22\\
\hline
\end{array}

\(\Rightarrow D\)