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Box-Plots and 5-Number Summary, SM-Bank 016

Ellyse recorded the number of wickets she took in the first seven games of the cricket season, which are as follows:

\(3, \ 5, \ 0, \ 8, \ 1, \ 2, \ 2 \)

  1. Complete the 5-number summary table of Ellyse's results below.   (2 marks)

\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}   \rule[-1ex]{0pt}{0pt} &  &  &  &  \\
\hline
\end{array}

  1. Draw a box plot, using the number line below for reference, that displays Ellyse's results.   (2 marks)
     

  1. Describe the skew of Ellyse's results.   (1 mark)

Show Answers Only

i.    \(\text{Ordering the data:}\ 0, \ 1, \ 2, \ 2, \ 3, \ 5, \ 8\)

\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} 0  \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 8 \\
\hline
\end{array}

ii.   
     

iii.   \(\text{Positively skewed}\)

Show Worked Solution

i.    \(\text{Ordering the data:}\ 0, \ 1, \ 2, \ 2, \ 3, \ 5, \ 8\)

\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} 0  \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 8 \\
\hline
\end{array}

ii.   
     

iii.   \(\text{Positively skewed}\)

Box Plots and 5-Number, SM-Bank 011

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Range}\ = 7 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Show Worked Solution

i.   \(\text{Range}\ = 7-0=7 \)
  

ii.   
         

\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}  0 \rule[-1ex]{0pt}{0pt} & 1 & 4 & 6 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Box Plots and 5-Number, SM-Bank 010

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Median}\ = 2 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Show Worked Solution

i.   \(\text{15 data points}\ \Rightarrow \ \text{Median = 8th data point}\)

\(\text{Median}\ = 2 \)
  

ii.   
           

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

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Box Plots and 5-Number, SM-Bank 005

Le Bron plays basketball and records the number of free throws he shoots in the first nine games of the season.

\(12, \ 8, \ 4, \ 15, \ 13, \ 7, \ 8, \ 3, \ 10\)

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

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Median}\ = 8\)

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

Show Worked Solution

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

\(3, \ 4, \ 7, \ 8, \ 8, \ 10, \ 12, \ 13, \ 15\)

\(\text{Median}\ = 8\)
 

ii.    \(\underbrace{3}_{\text{min}}, \ \underbrace{4, \ 7}_{Q1}, \ 8, \ \underbrace{8}_{Q2}, \ 10, \ \underbrace{12, \ 13}_{Q3}, \ \underbrace{15}_{\text{max}}\)

\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}  3 \rule[-1ex]{0pt}{0pt} & 5.5 & 8 & 12.5 & 15 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 12.5-5.5 =7\)

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

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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}

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

Box Plots and 5-Number, SM-Bank 003

The numerical data set below is made up of 9 data points.

\(1.1, \ 1.3, \ 1.3, \ 1.3, \ 1.6, \ 1.7, \ 1.9, \ 2.1, \ 2.1\)

Complete 5-number summary table below.   (2 marks)

\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}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\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}  1.1 \rule[-1ex]{0pt}{0pt} & 1.3 & 1.6 & 2.0 & 2.1 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{1.1}_{\text{min}}, \ \underbrace{1.3, \ 1.3}_{Q1}, \ 1.3, \ \underbrace{1.6}_{Q2}, \ 13, \ \underbrace{1.9, \ 2.1}_{Q3}, \ \underbrace{2.1}_{\text{max}}\)

\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}  1.1 \rule[-1ex]{0pt}{0pt} & 1.3 & 1.6 & 2.0 & 2.1 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 002

The numerical data set below is made up of 7 data points.

\(5, \ 7, \ 7, \ 10, \ 13, \ 15, \ 19\)

Complete 5-number summary table below.   (2 marks)

\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}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\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}  5 \rule[-1ex]{0pt}{0pt} & 7 & 10 & 15 & 19 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{5}_{\text{min}}, \ \underbrace{7}_{Q1}, \ 7, \ \underbrace{10}_{Q2}, \ 13, \ \underbrace{15}_{Q3}, \ \underbrace{19}_{\text{max}}\)

\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}  5 \rule[-1ex]{0pt}{0pt} & 7 & 10 & 15 & 19 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 001

The numerical data set below is made up of 11 data points.

\(2, \ 3, \ 3, \ 5, \ 8, \ 10, \ 11, \ 11, \ 12, \ 14, \ 16\)

Complete 5-number summary table below.   (2 marks)

\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}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\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}  2 \rule[-1ex]{0pt}{0pt} & 3 & 10 & 12 & 16 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{2}_{\text{min}}, \ 3, \ \underbrace{3}_{Q1}, \ 5, \ 8, \ \underbrace{10}_{Q2}, \ 11, \ 11, \ \underbrace{12}_{Q3}, \ 14, \ \underbrace{16}_{\text{max}}\)

\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}  2 \rule[-1ex]{0pt}{0pt} & 3 & 10 & 12 & 16 \\
\hline
\end{array}