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Displaying Data, SM-Bank 029

The graph shows the origin and type of all vehicles in a city.
 

  1.  Complete the table below using the graph.  (2 marks)
    \begin{array} {|l|c|c|c|}
    \hline
    \rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Sedans}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} & \textbf{Utility vehicles}\rule[-1ex]{0pt}{0pt} & \textbf{Trucks and vans}\\
    \hline
    \rule{0pt}{2.5ex} \textbf{Australian vehicles} \rule[-1ex]{0pt}{0pt} & \\
    \hline
    \rule{0pt}{2.5ex} \textbf{European vehicles} \rule[-1ex]{0pt}{0pt} &  \\
    \hline
    \rule{0pt}{2.5ex} \textbf{Asian vehicles} \rule[-1ex]{0pt}{0pt} &\\
    \hline
    \end{array}
  2. What was the total number of Asian vehicles in the city?  (1 mark)
  3. What was the total number of Trucks and vans in the city?  (1 mark)
  4. What percentage of all vehicles in the city were Australian vehicles? Give your answer correct to 1 decimal place.  (2 marks)
Show Answers Only

a.

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Sedans}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} & \textbf{Utility vehicles}\rule[-1ex]{0pt}{0pt} & \textbf{Trucks and vans}\\
\hline
\rule{0pt}{2.5ex} \textbf{Australian vehicles} \rule[-1ex]{0pt}{0pt} & 2000 & 1000 & 5000\\
\hline
\rule{0pt}{2.5ex} \textbf{European vehicles} \rule[-1ex]{0pt}{0pt} & 4000 & 3000 & 3000 \\
\hline
\rule{0pt}{2.5ex} \textbf{Asian vehicles} \rule[-1ex]{0pt}{0pt} & 5000 & 7000 & 7000\\
\hline
\end{array}

b.    \(19\ 000\)

c.    \(15\ 000\)

d.    \(21.6\%\)

Show Worked Solution

a.

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Sedans}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} & \textbf{Utility vehicles}\rule[-1ex]{0pt}{0pt} & \textbf{Trucks and vans}\\
\hline
\rule{0pt}{2.5ex} \textbf{Australian vehicles} \rule[-1ex]{0pt}{0pt} & 2000 & 1000 & 5000\\
\hline
\rule{0pt}{2.5ex} \textbf{European vehicles} \rule[-1ex]{0pt}{0pt} & 4000 & 3000 & 3000 \\
\hline
\rule{0pt}{2.5ex} \textbf{Asian vehicles} \rule[-1ex]{0pt}{0pt} & 5000 & 7000 & 7000\\
\hline
\end{array}

b.    \(\text{Total Asian vehicles}\)

\(=5000+7000+7000=19\ 000\)

c.    \(\text{Total Trucks and vans}\)

\(=5000+3000+7000=15\ 000\)

d.    \(\text{% Australian vehicles}\) \(=\Bigg(\dfrac{\text{Total Australian vehicles}}{\text{Total Sedans + Utilities + Trucks and vans}}\Bigg)\times 100\%\)
    \(=\Bigg(\dfrac{2000+1000+5000}{11\ 000+11\ 000+15\ 000}\Bigg)\times 100\%\)
    \(=\dfrac{8000}{37\ 000}\times 100\%\)
    \(=21.621\dots\%\)
    \(\approx 21.6\%\ \text{(1 d.p.)}\)