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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}`

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%.