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Interpreting Data, SM-Bank 006

Hannah is planning an Australian snowboarding trip this winter and is using the chart below to help decide when she should take her holidays and where she should go.
 

Hannah wishes to compare the 2 resorts using statistical information.

  1. Complete the statistical information in the table below.  (2 marks)
     
    \begin{array} {|l|c|c|}
    \hline
    \rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 1}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 2}\ \ \ \ \ \ \  \\
    \hline
    \rule{0pt}{2.5ex} \textbf{Range of snowfall (cm)} \rule[-1ex]{0pt}{0pt}&  & \\
    \hline
    \rule{0pt}{2.5ex} \textbf{Mean of snowfall (cm)} \rule[-1ex]{0pt}{0pt} &   &  \\
    \hline
    \rule{0pt}{2.5ex} \textbf{Median of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & &  \\
    \hline
    \end{array}

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  2. Using your results in the table above (a), which resort should Hannah choose to visit for her snowboarding holiday?
    Justify your answer with at least 1 reference to the table.  (1 mark)

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  3. Complete the table below, and use it to decide in which month Hannah should book her snowboarding holiday?
    Justify your answer with at least 1 reference to the table and 1 to the graph.  (3 marks)

    \begin{array} {|l|c|c|}
    \hline
    \rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Mean Snowfall}\ \ \ \ \ \ \    \\
    \hline
    \rule{0pt}{2.5ex} \textbf{June} \rule[-1ex]{0pt}{0pt}& \\
    \hline
    \rule{0pt}{2.5ex} \textbf{July} \rule[-1ex]{0pt}{0pt} &  \\
    \hline
    \rule{0pt}{2.5ex} \textbf{August} \rule[-1ex]{0pt}{0pt} & \\
    \hline
    \rule{0pt}{2.5ex} \textbf{September} \rule[-1ex]{0pt}{0pt} & \\
    \hline
    \end{array}

    --- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

a.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 1}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 2}\ \ \ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} \textbf{Range of snowfall (cm)} \rule[-1ex]{0pt}{0pt} &7 &10\\
\hline
\rule{0pt}{2.5ex} \textbf{Mean of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & 10.5  & 10.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Median of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & 14 & 13.5 \\
\hline
\end{array}

b.    \(\text{See worked solution}\)

c.  

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Mean Snowfall}\ \ \ \ \ \ \    \\
\hline
\rule{0pt}{2.5ex} \textbf{June} \rule[-1ex]{0pt}{0pt}& 6.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{July} \rule[-1ex]{0pt}{0pt} & 13.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{August} \rule[-1ex]{0pt}{0pt} & 16\\
\hline
\rule{0pt}{2.5ex} \textbf{September} \rule[-1ex]{0pt}{0pt} & 8\\
\hline
\end{array}

\(\text{See worked solution}\)

Show Worked Solution

a.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 1}\ \ \ \ \ \ \  \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Resort 2}\ \ \ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} \textbf{Range of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & 14-7=7 & 17-7=10\\
\hline
\rule{0pt}{2.5ex} \textbf{Mean of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & \dfrac{6+14+13+9}{4}=10.5  & \dfrac{7+11+17+7}{4}=10.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Median of snowfall (cm)} \rule[-1ex]{0pt}{0pt} & \dfrac{11+17}{2}=14 & \dfrac{14+13}{2}=13.5 \\
\hline
\end{array}

 

b.    \(\text{The mean snowfall for both resorts is the same.}\)

\(\text{The median snowfall for Resort 2 is higher than Resort 1.}\)

\(\text{The range of snowfall for Resort 2 is higher than Resort 1.}\)

\(\text{Based on these findings Hannah should choose Resort 2.}\)

c.   

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt} &\ \ \ \ \ \ \  \textbf{Mean Snowfall}\ \ \ \ \ \ \    \\
\hline
\rule{0pt}{2.5ex} \textbf{June} \rule[-1ex]{0pt}{0pt}& \dfrac{6+7}{2}=6.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{July} \rule[-1ex]{0pt}{0pt} & \dfrac{14+13}{2}=13.5 \\
\hline
\rule{0pt}{2.5ex} \textbf{August} \rule[-1ex]{0pt}{0pt} & \dfrac{15+17}{2}=16\\
\hline
\rule{0pt}{2.5ex} \textbf{September} \rule[-1ex]{0pt}{0pt} & \dfrac{9+7}{2}=8\\
\hline
\end{array}

 
\(\text{Based on both the information in the graph and the table above,}\)

\(\text{Hannah should holiday in August.}\)

\(\text{The mean snowfall is highest in this month from the table}\)

\(\text{and, from the graph, Resort 2 has its highest snowfall in August which is 3 cm}\)

\(\text{than Resort 1’s highest in July.}\)

Filed Under: Interpreting Data Tagged With: num-title-ct-core, smc-5077-15-Reading graphs, smc-5077-25-Mean Median Mode Range

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