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Statistics, STD2 EQ-Bank 03 MC

For the data below, which is the correct five figure summary?

\(12,\ \ 16, \ \ 4,\ \ 6, \ \ 4, \ \ 5, \ \  22, \ \ 20, \ \ 12, \ 8\ \)

  1. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 21\)
  2. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 22\)
  3. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 21\)
  4. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 22\)
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\(D\)

Show Worked Solution

\(\text{Ordered data set}\ \rightarrow\ \ 4,\ \ 4, \ \ 5,\ \ 6, \ \ 8, \ \ 12, \ \  12, \ \ 16, \ \ 20, \ 22\ \)

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  4\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  \dfrac{8+12}{2}=10\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  22\\
\hline
\end{array}

\(\Rightarrow D\)

Statistics, STD2 EQ-Bank 01

A Physics class of  12 students is going on a 4 day excursion by bus.

The students are asked to each pack one bag for the trip. The bags are weighed, and the weights (in kg) are listed in order as follows:

\(8,\ \ 9, \ \ 10,\ \ 10, \ \ 15, \ \  18, \ \  22, \ \ 25, \ \ 29, \ \ 35, \ \ 38, \ \ 41 \)

  1. Use the above data to produce a five number summary for the weights of the bags.   (2 marks)
  3. Using your five number summary from part (a), calculate the interquartile range of the weights.   (2 marks)
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a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(22\)

Show Worked Solution

a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(\text{IQR}\) \(=Q_3-Q_1\)
    \(=32-10=22\)