Box Plots and 5-Number, SM-Bank 004

Robert records the total goals scored in each of the first 11 matches of his favourite soccer team.

\(3, \ 5, \ 1, \ 2, \ 2, \ 7, \ 6, \ 4, \ 1, \ 5, \ 3\)

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

the range (1 mark)

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the interquartile range (2 marks)

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Show Answers Only

i. \(\text{Range}\ = 7-1=6\)

ii. \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)

Show Worked Solution

i. \(\text{Ordering the data values:}\)

\(1, \ 1, \ 2, \ 2, \ 3, \ 3, \ 4, \ 5, \ 5, \ 6, \ 7\)

\(\text{Range}\ = 7-1=6\)

ii. \(\underbrace{1}_{\text{min}}, 1, \ \underbrace{2}_{Q1}, \ 2, \ 3, \ \underbrace{3}_{Q2}, \ 4, \ 5, \ \underbrace{5}_{Q3}, \ 6, \ \underbrace{7}_{\text{max}}\)

\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} 1 \rule[-1ex]{0pt}{0pt} & 2 & 3 & 5 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)