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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 009

Yoyo was practicing his cello for an orchestra audition and the data set below records the number of hours he practiced each day over a 10-day period.

\(7.6, \ 12.2, \ 8.4, \ 7.8, \ 8.8, \ 9.3, \ 11.9, \ 7.0, \ 8.2, \ 10.4\)

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.    \(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

Show Worked Solution

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

\(7.0, \ 7.6, \ 7.8, \ 8.2, \ 8.4, \ 8.8, \ 9.3, \ 10.4, \ 11.9, \ 12.2\)

\(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.    \(\underbrace{7.0}_{\text{min}}, \ 7.7, \ \underbrace{7.8}_{Q1}, \ 8.2, \ \underbrace{8.4, \ 8.8}_{Q2}, \ 9.3, \ \underbrace{10.4}_{Q3}, \ 11.9, \ \underbrace{12.2}_{\text{max}}\)

\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}  7.0 \rule[-1ex]{0pt}{0pt} & 7.8 & 8.6 & 10.4 & 12.2 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

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

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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}

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

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}

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