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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 Summary, SM-Bank 015

Eli sat 22 Maths quizzes throughout year 8 and her results were recorded in the 5-number summary below.

\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}  30 \rule[-1ex]{0pt}{0pt} & 50 & 60 & 70 & 80 \\
\hline
\end{array}

  1. Using the number line below as reference, draw a box plot that displays Eli's results.   (2 marks)
     

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

Show Answers Only

i.    
       

ii.    \(\text{Negatively skewed (slightly)}\)

Show Worked Solution

i.    
       

ii.    \(\text{Negatively skewed (slightly)}\)

Box Plots and 5-Number Summary, SM-Bank 014

The test results in English and Mathematics for a class were recorded and displayed in the box plots.
 

  1. What is the interquartile range for English?   (1 mark)

  2. Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of their centres and spread.   (3 marks)

Show Answers Only

i.    `text{IQR}_text{(English)}\ = 80-50=30`

ii.  `text(Skewness)`

  • `text(English has greater negative skew)`
  • `text(Maths is more normally distributed)`

`text(Location and Spread)`

  • `text(English has a range of 85, Maths has 40.)`
  • `text{English has larger IQR than Maths (30 vs 15)}`
  • `text{Maths’ median (75) is higher than English (70)}`
  • `text{Same upper quartile marks (80)}`
  • `text(English has highest and lowest individual mark)`
Show Worked Solution

i.    `text{IQR}_text{(English)}\ = 80-50=30`

 

♦ Mean mark (ii) 35%
COMMENT: The best answers use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

ii.  `text(Skewness)`

  • `text(English has greater negative skew)`
  • `text(Maths is more normally distributed)`

`text(Location and Spread)`

  • `text(English has a range of 85, Maths has 40.)`
  • `text{English has larger IQR than Maths (30 vs 15)}`
  • `text{Maths’ median (75) is higher than English (70)}`
  • `text{Same upper quartile marks (80)}`
  • `text(English has highest and lowest individual mark)`

Box Plots and 5-Number Summary, SM-Bank 013

Terry and Kim each sat twenty class tests. Terry’s results on the tests are displayed in the box plot shown in part (i).

  1. Kim’s  5-number summary for the tests is  67,  69,  71,  73,  75.

     

    Draw a box plot to display Kim’s results below that of Terry’s results.   (1 mark)
     
       

  2. What percentage of Terry’s results were below 69?     (1 mark)

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

Show Answers Only
i.    

ii.  `text(50%)`
 

iii.  `text{By inspection of box plot: Evenly skewed}`

Show Worked Solution
i. 

 
ii.  `text(50%)`
 

iii.  `text{By inspection of box plot: Evenly 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 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 007

The data set below consists of 8 data points.

\(7.0, \ 7.4, \ 8.1, \ 9.3, \ 9.5, \ 10.7, \ 11.1, \ 12.9 \)

Complete the 5-number summary table of the data set 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}  7.0 \rule[-1ex]{0pt}{0pt} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{7.0}_{\text{min}}, \underbrace{7.4,\ 8.1}_{Q1}, \ \underbrace{9.3, \ 9.5}_{Q2}, \ \underbrace{10.7, \ 11.1}_{Q3}, \ \underbrace{12.9}_{\text{max}}\)

\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} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 006

Rocket Reddy played 10 full seasons of first grade rugby league and recorded the number of tries he scored each season.

\(13, \ 5, \ 11, \ 2, \ 10, \ 13, \ 5, \ 7, \ 8, \ 3\)

Complete the 5-number summary table of Rocket Reddy's data 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

\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)

\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} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}

Show Worked Solution

\(\text{Place data points in order:}\)

\(2, \ 3, \ 5, \ 5, \ 7, \ 8, \ 10, \ 11, \ 13, \ 13\)

\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)

\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} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}

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}

Statistics, STD2 S1 SM-Bank 2 MC

A dataset has the following five-number summary.

If the range of the dataset is 8, what is the minimum value of the dataset?

  1.  2
  2.  3
  3.  4
  4.  7
Show Answers Only

`D`

Show Worked Solution
`text(Range)` `=\ text{Max}-text{Min}`
`8` `= 15-text{Min Value}`
`:.\ text{Min}` `= 15-8`
  `=7`

 
`=> D`

Statistics, STD2 S1 SM-Bank 1

Write down the five-number summary for the dataset 

`3, \ 7, \ 8, \ 11, \ 13, \ 18.`  (2 marks)

Show Answers Only
`text(Minimum value:)`   `3`
`text(First quartile:)`   `7`
`text(Median:)`   `(11 + 8)/2 = 9.5`
`text(Third quartile:)`   `13`
`text(Maximum value:)`   `18`
Show Worked Solution
`text(Minimum value:)`   `3`
`text(First quartile:)`   `7`
`text(Median:)`   `(11 + 8)/2 = 9.5`
`text(Third quartile:)`   `13`
`text(Maximum value:)`   `18`

Statistics, STD2 S1 2017 HSC 1 MC

The box-and-whisker plot for a set of data is shown.
 

What is the median of this set of data?

  1. 15
  2. 20
  3. 30
  4. 35
Show Answers Only

`C`

Show Worked Solution

`text(Median = 30)`

`=> C`

Statistics, STD2 S1 2016 HSC 22 MC

The box-and-whisker plots show the results of a History test and a Geography test.
 

In History, 112 students completed the test. The number of students who scored above 30 marks was the same for the History test and the Geography test.

How many students completed the Geography test?

  1. 8
  2. 50
  3. 56
  4. 112
Show Answers Only

`=> C`

Show Worked Solution

`text{In History} \ => \  text{Q}_3 = 30\ \text{marks}`

`:.\ text{Scoring over 30}\ = 25text(%) xx 112 = 28\ \text{students}`
 

`text{In Geography} \ => \ text{Median}\ = 30\ \text{marks}`

`:.\ text{Students completing Geography}\ =2 xx 28 = 56\ \text{students}`

`=> C`

Statistics, STD2 S1 2016 HSC 19 MC

A soccer referee wrote down the number of goals scored in 9 different games during the season.

`2,  \ 3,  \ 3,  \ 3,  \ 5,  \ 5,  \ 8,  \ 9,  \ ...`

The last number has been omitted. The range of the data is 10.

What is the five-number summary for this data set?

  1. `2, 3, 5, 8.5, 12`
  2. `2, 3, 5, 8.5, 10`
  3. `2, 3, 5, 8, 12`
  4. `2, 3, 5, 8, 10`
Show Answers Only

`=> A`

Show Worked Solution

`text{Since range is 10} \ => \ text{Last data point = 12}`

`text{Q}_1 = 3`

`text{Q}_3 = (8 + 9)/2 = 8.5`

`text(Median = 5)`

`=> A`

♦ Mean mark 46%.

Statistics, STD2 S1 2015 HSC 6 MC

The times, in minutes, that a large group of students spend on exercise per day are presented in the box‑and‑whisker plot.
 

What percentage of these students spend between 40 minutes and 60 minutes per day on exercise?

  1. 17%
  2. 20%
  3. 25%
  4. 50%
Show Answers Only

`C`

Show Worked Solution

`text{Q}_1 = 40, \ text(Median) = 60`

`:.\ text(% Students between 40 and 60)`

`= 50text{%}-25text{%}`

`=25 text{%}`
 

`=>C`

Statistics, STD2 S1 2005 HSC 22 MC

Two groups of people were surveyed about their weekly wages. The results are shown in the box-and-whisker plots.
 

Which of the following statements is true for the people surveyed?

  1. The same percentage of people in each group earned more than $325 per week.
  2. Approximately 75% of people under 21 years earned less than $350 per week.
  3. Approximately 75% of people 21 years and older earned more than $350 per week.
  4. Approximately 50% of people in each group earned between $325 and $350 per week.
Show Answers Only

`B`

Show Worked Solution

`text{Option A: 50% of Under 21 group earned over $325 and 75%}`

`text{of Over 21 group did. NOT TRUE.}`
 

`text{Option B: 75% of Under 21 group earned below $350 is TRUE.}`
 

`text{Options C and D: can both be proven to be untrue using their}`

`text{median and quartile values.}`

`=>  B`

Statistics, STD2 S1 2008 HSC 10 MC

The marks for a Science test and a Mathematics test are presented in box-and-whisker plots.
 

 Which measure must be the same for both tests?

  1. Mean
  2. Range
  3. Median
  4. Interquartile range
Show Answers Only

`D`

Show Worked Solution

`text(IQR)=text(Upper Quartile)-text(Lower Quartile)`

`text{In both box plots, IQR = 3 intervals (against bottom scale)}`

`=>  D`

Statistics, STD2 S1 2010 HSC 27b

The graphs show the distribution of the ages of children in Numbertown in 2000 and 2010.
  

  1. In 2000 there were 1750 children aged 0–18 years.

     

    How many children were aged 12–18 years in 2000?   (1 mark)

  2. The number of children aged 12–18 years is the same in both 2000 and 2010.

     

    How many children aged 0–18 years are there in 2010?    (1 mark)

  3. Identify TWO changes in the distribution of ages between 2000 and 2010. In your answer, refer to measures of location or spread or the shape of the distributions.   (2 marks)

  4. What would be ONE possible implication for government planning, as a consequence of this change in the distribution of ages?   (1 mark)

Show Answers Only

i.    `875`

ii.    `3500`

iii.  `text{Changes in distribution (include 2 of the following):}`

  • `text(the lower quartile age is lower in 2010)`
  • `text(the median is lower in 2010)`
  • `text(the upper quartile age is lower in 2010)`
  • `text(the interquartile range is greater in 2010)`
  • `text(2010 is positively skewed while 2000 is negatively)`

iv.  `text(Implication for government planning:)`

`text(Since the children are getting younger in 2010,)`

  • `text(Approve and build more childcare facilities)`
  • `text(Build more school and public playgrounds)`
Show Worked Solution

i.    `text{Since the median = 12 years}`

♦ Mean mark (i) 45%

`=>\ text{50% of children are aged 12–18 years}`

`:.\ text{Children aged 12–18}\ = 50\text{%}\ xx 1750 = 875`

 

♦♦ Mean mark (ii) 25%

ii.   `text{Upper quartile (2010) = 12 years}`

`text{Children in upper quartile = 875 (from part (i))}`

`:.\ text{Children aged 0–18}\ =4 xx 875= 3500`
 

iii.  `text{Changes in distribution (include 2 of the following):}`

♦ Mean mark (iii) 35%
MARKER’S COMMENT: A number of students incorrectly identified “positive” skew as “negative” skew here.
  • `text(the lower quartile age is lower in 2010)`
  • `text(the median is lower in 2010)`
  • `text(the upper quartile age is lower in 2010)`
  • `text(the interquartile range is greater in 2010)`
  • `text(2010 is positively skewed while 2000 is negatively)`

iv.  `text(Implication for government planning:)`

♦ Mean mark (iv) 46%
MARKER’S COMMENT: Answers should reflect the 1 mark allocation.

`text(Since the children are getting younger in 2010,)`

  • `text(Approve and build more childcare facilities)`
  • `text(Build more school and public playgrounds)`

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
Show Answers Only

`B`

Show Worked Solution

`text{Since the median (155) is closer to the lower quartile (150) and range}`

`text{low (140) than the upper quartile (190) and range high (200), it is}`

`text{positively skewed.}`

`=>B`

♦ Mean mark 47%.