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

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