Data Analysis, SM-Bank 054

The following ordered stem plot shows the areas, in square kilometres, of 27 suburbs of a large city.

\begin{array} {r|lll}
\textbf{Stem} & \textbf{Leaf} \\
\hline 1 & 5\ 6\ 7\ 8 \\
2 & 1\ 2\ 4\ 5 \ 6\ 8\ 9\ 9 \\
3 & 0\ 1\ 1\ 2\ 2\ 8\ 9 \\
4 & 0\ 4\ 7 \\
5 & 0\ 1 \\
6 & 1\ 9 \\
7 & \\
8 & 4 \\
\end{array}

\(\text{key: }1|6=1.6\ \text{km}^2\)

For these suburbs
i. What is the median, in square kilometres? (1 mark)

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ii. What is the range, in square kilometres? (1 mark)

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What is the possible outlier? (1 mark)
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Briefly describe the skewness of the data. (1 mark)
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Show Answers Only

a. i. \(3.1\ \text{km}^2\)

ii. \(6.9\)

b. \(8.4\ \text{km}^2\)

c. \(\text{Positively skewed.}\)

Show Worked Solution

a.	i.	\(\text{Median}\)	\(=\dfrac{27+1}{2}\)
			\(=\ \text{14 th score}\)
		\(\therefore\ \text{Median}\)	\(=3.1\ \text{km}^2\)

	ii.	\(\text{Range}\)	\(=8.4-1.5\)
			\(=6.9\)

b. \(8.4\ \text{km}^2\ \text{is a possible outlier}\)

c. \(\text{The data is positively skewed as the tail is to the right.}\)