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Displaying Data, SM-Bank 031

  1. Draw an ordered stem-and-leaf plot for the following set of scores.
     
    \(51\ \ \ \ \ 56\ \ \ \ \ 58\ \ \ \ \ 36\ \ \ \ \ 28\ \ \ \ \ 45\ \ \ \ \ 53\ \ \ \ \ 69\ \ \ \ \ 47\ \ \ \ \ 52\)     (2 marks)

  2. What is the median of the set of scores?   (1 mark)

  3. Comment on the skewness of the set of scores.   (1 mark)

Show Answers Only
a.    \begin{array} {r|lll} \textbf{Stem} & \textbf{Leaf} \\ \hline 2 & 8 \\ 3 & 6 \ \\ 4 & 5\ 7\\ 5 & 1\ 2\ 3\ 6 \ 8 \\ 6 & 9 \\ \end{array}

b.    \(51.5\)

c.    \(\text{The data has a tail that stretches to the left}\)

\(\therefore\ \text{Data is negatively skewed.}\)

Show Worked Solution
a.    \begin{array} {r|lll} \textbf{Stem} & \textbf{Leaf} \\ \hline 2 & 8 \\ 3 & 6 \ \\ 4 & 5\ 7\\ 5 & 1\ 2\ 3\ 6 \ 8 \\ 6 & 9 \\ \end{array}

 

b.    \(\text{10 scores}\)

\(\therefore\ \text{Median}\) \(=\dfrac{\text{(5th + 6th)}}{2}\)
  \(=\dfrac{51 + 52}{2}\)
  \(=51.5\)

 

c.    \(\text{The data has a tail that stretches to the left}\)

\(\therefore\ \text{Data is negatively skewed.}\)

Statistics, STD2 S1 2005 HSC 24a

  1. Draw a stem-and-leaf plot for the following set of scores.

  2.  

     

    `21\ \ \ 45\ \ \ 29\ \ \ 27\ \ \ 19\ \ \ 35\ \ \ 23\ \ \ 58\ \ \ 34\ \ \ 27`  (2 marks)

  3. What is the median of the set of scores?   (1 mark)

  4. Comment on the skewness of the set of scores.   (1 mark)

Show Answers Only
  1.  
  2. `28`
  3. `text(The data has a tail that stretches to the right)`

  4.  

    `:.\ text(Data is positively Skewed.)`

Show Worked Solution
i.    HSC 2005 24a

 

ii.  `text(10 scores)`

`:.\ text(Median)` `= text{(5th + 6th)}/2`
  `= (27 + 29)/2`
  `= 28`

 

iii.  `text(The data has a tail that stretches to the right)`

`:.\ text(Data is positively skewed.)`