Box Plots and 5-Number, SM-Bank 008

Matt records the number of times he takes his dog Max for a walk each month. The data set below records the months January to August.

\(21, \ 24, \ 28, \ 22, \ 15, \ 12, \ 13, \ 17\)

Using a 5-number summary of this dataset, or otherwise, determine

the median (1 mark)

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the interquartile range (2 marks)

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Show Answers Only

i. \(\text{Median}\ = \dfrac{17+21}{2} = 19 \)

ii. \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)

Show Worked Solution

i. \(\text{Placing data values in order:}\)

\(12, \ 13, \ 15, \ 17, \ 21, \ 22, \ 24, \ 28 \)

\(\text{Median}\ = \dfrac{17+21}{2} = 19 \)

ii. \(\underbrace{12}_{\text{min}}, \underbrace{13+15}_{Q1}, \ \underbrace{17+21}_{Q2}, \ \underbrace{22, \ 24}_{Q3}, \ \underbrace{28}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex} 12 \rule[-1ex]{0pt}{0pt} & 14 & 19 & 23 & 28 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)