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Interpreting Data, SM-Bank 031

Judge recorded 2 hourly temperatures from the Bureau of Meteorology for his home town, for a 24 hour period beginning at midnight.

  1. What was the temperature at 2 a.m.?  (1 mark)
  2. At what time was the minimum temperature for the 24 hour period?  (1 mark)
  3. What was the range of temperatures?  (1 mark)
  4. Use the graph to estimate the 2 times of the day when the temperature was 18°C?  (1 mark)

  5. Use the graph to estimate the temperature at:
    i.    7:00 a.m.  (1 mark)

    ii.   9:30 a.m.  (1 mark)

    iii.  5:00 p.m.  (1 mark)

Show Answers Only

a.    \(13 ^{\circ }\text{C}\)

b.    \(6:00\ \text{a.m.}\)

c.    \(16^{\circ }\text{C}\)

d.    \(9:00\ \text{a.m. and }9:30\ \text{p.m.}\)

e.    i.    \(12 ^{\circ }\text{C}\)

ii.   \(20 ^{\circ }\text{C}\)

iii.  \(25 ^{\circ }\text{C}\)

Show Worked Solution

a.    \(13 ^{\circ }\text{C}\)

b.    \(6:00\ \text{a.m.}\)

c.    \(16^{\circ }\text{C}\)

d.    \(9:00\ \text{a.m. and }9:30\ \text{p.m.}\)

e.    i.    \(12 ^{\circ }\text{C}\)

ii.   \(20 ^{\circ }\text{C}\)

iii.  \(25 ^{\circ }\text{C}\)

Interpreting Data, SM-Bank 029 MC

Students at a high school were surveyed to find whether they did exercise before school.

The graph below shows the results.
 


 

There were 150 17-year-old students at the high school.

How many 17-year-old students responded 'Every Day'?

  1. 14
  2. 30
  3. 38
  4. 45
Show Answers Only

\(D\)

Show Worked Solution

\(\text{30% of 17-year-old responded ‘Every Day’.}\)

\(\therefore\ \text{Number}\) \(=0.3\times 150\)
  \(=45\)

 
\(\Rightarrow D\)

Interpreting Data, SM-Bank 028 MC

Gavin measured the temperature every 3 hours from 6:00 am to 3:00 pm.
 

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Time of the day} \rule[-1ex]{0pt}{0pt} & \text{6:00 am}& \text{9:00 am} & \text{12:00 pm} & \text{3:00 pm} \\
\hline
\rule{0pt}{2.5ex} \text{Temperature (°C)} \rule[-1ex]{0pt}{0pt} & 22&28&32&29 \\
\hline
\end{array}

 

Which graph shows Gavin's results?

A. B. C. D.
Show Answers Only

\(D\)

Show Worked Solution

\(\Rightarrow D\)

Interpreting Data, SM-Bank 027

The goals scored by 4 players in a season of water polo were recorded in the graph below.

Will scored 8 goals in the season.

Sam scored 5 goals.

How many more goals did Bilbo score than Ginili?  (2 marks)

Show Answers Only

\(7\ \text{more goals}\)

Show Worked Solution

\(\text{Since Will scored 8 goals,}\)

\(= 2\ \text{goals}\)

\(\longrightarrow\ \text{Bilbo scored 10 goals}\)

\(\longrightarrow\ \text{Ginili scored 3 goals}\)

\(\therefore\ \text{Bilbo scored 7 more goals than Ginili.}\)

Interpreting Data, SM-Bank 026

Matt and Libby planted 50 trees each over 3 weeks.

The bar chart below shows the amount of trees each planted in each week.
 

How many more trees did Libby plant than Matt in Week 2.  (2 marks)

Show Answers Only

\(5\)

Show Worked Solution

\(\text{Trees planted by Matt in Week 2}\)

\(= 35-15\)

\(= 20\)
 

\(\text{Trees planted by Libby in Week 2}\)

\(= 45-20\)

\(= 25\)
 

\(\therefore\ \text{Libby planted 5 more trees than Matt in Week 2.}\)

Interpreting Data, SM-Bank 025 MC

Camilla asked each student in four year 7 classes if they played soccer.

She recorded the results in the graph below. 
 

 
Which class had the highest number of students that played soccer?

  1. Class A
  2. Class B
  3. Class C
  4. Class D
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Consider each option:}\)

\(\text{Class A}: 8+6=14\)

\(\text{Class B}: 10+3=13\)

\(\text{Class C}: 4+9=13\)

\(\text{Class D}: 11+2=13\)

\(\therefore\ \text{Class A has the most soccer players.}\)

\(\Rightarrow A\)

Interpreting Data, SM-Bank 023

32 students are shown 5 colours and they choose their favourite.

The fractions in the graph below show how the students voted.

How many more students voted for green than blue?  (2 marks)

Show Answers Only

\(4\)

Show Worked Solution
\(\text{Votes for green}\) \(=\dfrac{1}{4}\times 32\)
  \(=8\)
   
\(\text{Votes for blue}\) \(=\dfrac{1}{8}\times 32\)
  \(=4\)

 

\(\therefore\ \text{4 more students voted for green than blue.}\)

Interpreting Data, SM-Bank 022 MC

This graph shows the number of men and women that registered to vote before a council election on different days of the week.
  

On which day is the difference between the number of men and women registering closest to 50?

  1. Monday
  2. Tuesday
  3. Wednesday
  4. Friday
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Each interval = 20 people}\)

\(\text{Difference needs to be 2.5 intervals}\)

\(\therefore\ \text{Tuesday is closest}\)

 
\(\Rightarrow B\)

Interpreting Data, SM-Bank 021 MC

Aaron went on holiday and spent his money on accommodation, golf and meals.

He spent $1500 in total and the pie chart below shows how he spent it.
 

 
How much money did Aaron spend on meals on his holiday?

  1. $225
  2. $375
  3. $425
  4. $600
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Percentage spent on accommodation}\)

\(=\dfrac{675}{1500}\times 100\)

\(=45\%\)
 

\(\rightarrow\ \text{Percentage on meals}=100-(40+45)=15\%\)

\(\therefore\ \text{Amount spent on meals}\)

\(=15\%\times 1500\)

\(=$225\)

\(\Rightarrow A\)

Interpreting Data, SM-Bank 020 MC

This graph shows the number of cockatoos in a gum tree at 15 minute intervals over 4 hours.
 

 
At which time were the lowest number of cockatoos in the gum tree?

  1. 3:00
  2. 3:15
  3. 3:45
  4. 4:00
Show Answers Only

\(C\)

Show Worked Solution

\(\text{The lowest data point is one interval before 4:00 pm.}\)

\(\therefore\ \text{The lowest number were in the tree at 3:45 pm.}\)

\(\Rightarrow C\)

Interpreting Data, SM-Bank 019 MC

The graph below shows the number of people in a supermarket at 15-minute intervals during a 4 hour period.
 


 

What time were the greatest amount of people in the supermarket?

  1. 11:15 AM
  2. 12:00 PM
  3. 12:30 PM
  4. 1:45 PM

Show Answers Only

\(B\)

Show Worked Solution

\(\therefore\ \text{The highest data point in the graph is at 12:00 PM}\)
 

\(\Rightarrow B\)

Interpreting Data, SM-Bank 017

Body mass index (BMI), in kilograms per square metre, was recorded for a sample of 32 men and displayed in the ordered stem plot below.
  

  1. Describe the shape of the distribution.  (1 mark)

  2. Determine the median BMI for this group of men.  (1 mark)

  3. People with a BMI of 25 or over are considered to be overweight.
  4. What percentage of these men would be considered to be overweight?  (1 mark)

Show Answers Only

a.    \(\text{Positively skewed}\)

b.    \(24.55\)

c.    \(37.5\%\)

Show Worked Solution

a.   \(\text{The tail is to the right, therefore positively skewed}\)
 

b.   \(32\ \text{data points}\)

\(\text{Median}\) \(=\dfrac{\text{(16th + 17th)}}{2}\)
  \(=\dfrac{ (24.5 + 24.6)}{2}\)
  \(= 24.55\)

 

c.    \(\text{Percentage}\) \(=\dfrac{12}{32}\times 100\)
    \(=37.5\%\)

Interpreting Data, SM-Bank 016 MC

A single back-to-back stem-and-leaf plot would be an appropriate graphical tool to investigate the association between a car’s speed, in kilometres per hour, and the

  1. driver’s age, in years. 
  2. car’s colour (white, red, grey, other). 
  3. average distance travelled, in kilometres.
  4. driver’s sex (female, male).
Show Answers Only

\(D\)

Show Worked Solution

\(\text{In a back-to-back stem-and-leaf plot, the numerical }\)

\(\text{speed data has to be plotted against categorical data}\)

\(\text{with two options.}\)

\(\therefore\ \text{Driver’s sex (M or F)}\)

\(\Rightarrow D\)

Interpreting Data, SM-Bank 015 MC

The back-to-back ordered stem-and-leaf plot below shows the distribution of maximum temperatures (in °Celsius) of two towns, Beachside and Flattown, over 21 days in January.
 


 

For this distribution, which of the following is not true?

  1. The range of temperatures for Flattown is greater than the range of temperatures for Beachside.
  2. The median temperature for Beachside is lower than the median temperature for Flatttown.
  3. The distribution of temperatures for Beachside is positively skewed.
  4. The maximum temperatures for Flattown are generally lower than those of Beachside.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Options A}\ \rightarrow\ \text{Flattown Range}=28,\ \ \text{Beachside Range}=23\ \checkmark\)

\(\text{Options B}\ \rightarrow\ \text{Flattown Median}=37,\ \ \text{Beachside Median}=23\ \checkmark\)

\(\text{Options C}\ \rightarrow \ \text{Beachside distribution has a tail to the right, so positively skewed}\ \checkmark\)

\(\text{Options D}\ \rightarrow \ \text{Flattown has 8 max temps that are}\geq\ \text{to those of Beachside.  ×}\)
 

\(\Rightarrow D\)

Interpreting Data, SM-Bank 013 MC

The back-to-back ordered stem plot below shows the female and male smoking rates, expressed as a percentage, in 18 countries.
 

  

For these 18 countries, the smoking rates for females are generally

  1. lower and less variable than the smoking rates for males.
  2. lower and more variable than the smoking rates for males.
  3. higher and less variable than the smoking rates for males.
  4. higher and more variable than the smoking rates for males.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Smoking rates are lower and less variable (range of}\)

\(\text{females rates vs male rates is 13% vs 30%).}\)

\(\Rightarrow A\)

Interpreting Data, SM-Bank 011

Table 1 shows the number of rainy days recorded in a high rainfall area for each month during 2022.
 

CORE, FUR2 2009 VCAA 11

 

The dot plot below displays the distribution of the number of rainy days for the 12 months of 2008.
 

CORE, FUR2 2009 VCAA 12
 

  1. Circle the dot on the dot plot that represents the number of rainy days in April 2008.  (1 mark)

  2. For the year 2022, determine

     

i.  the median number of rainy days per month  (1 mark)

    1. the percentage of months that have more than 10 rainy days. Write your answer correct to the nearest percent.  (2 marks) 

Show Answers Only

 a.

CORE, FUR2 2009 VCAA 12 Answer

b.    i.    \(15.5\)

ii.    \(92\%\)

Show Worked Solution
a.    CORE, FUR2 2009 VCAA 12 Answer

 

b.i.    \(\text{Median}\) \(=\text{(6th + 7th)}/2\)
    \(=\dfrac{(15+16)}{2}\)
    \(=15.5\)

 

b.ii.   \(\text{Months with more than 10 rainy days}\)

\(=\dfrac{11}{12}\times 100\%\)

\(=91.66\dots\)

\(\approx 92\%\ \text{(nearest %)}\)

Interpreting Data, SM-Bank 010 MC

Kerri-anne records the temperature on her verandah at hourly intervals for a 24 hour period.

Which type of graph would best display this data so Kerri-anne could easily see the temperature fluctuations throughout the day?

  1. A sector graph
  2. A stem-and-leaf plot
  3. A column graph
  4. A line graph
Show Answers Only

\(D\)

Show Worked Solution

\(\text{A line graph shows variations over time.}\)

\(\Rightarrow D\)

Interpreting Data, SM-Bank 009 MC

Michael wants to record how he used the data on his phone last week. He spent time on social media, playing games and listening to music.

Which type of graph would best display this data so Michael could easily see the proportion of time spent on each activity?

  1. A sector graph
  2. A stem-and-leaf plot
  3. A column graph
  4. A dot plot
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Sector graph}\)

\(\Rightarrow A\)

Interpreting Data, SM-Bank 008 MC

At the school cross country carnival, the times of the 15 year of girls and boys were recorded.

Which type of graph would best display this data to enable a comparison of the performance of both groups?

  1. A sector graph
  2. Back-to-back stem-and-leaf plot
  3. A column graph
  4. A dot plot
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Back-to-back stem-and-leaf plot}\)

\(\Rightarrow B\)

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}
  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)

  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}

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}

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

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

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

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

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

Interpreting Data, SM-Bank 004

Bonn saved $2400 for his annual holiday.

He has drawn the graph below to represent his weekly holiday spending.

  1. What type of graph has been used to display the information?  (1 mark)
  2. Identify the two variables Bonn has used in this graph?  (1 mark)
  3. What is the amount per week that Bonn is expecting to spend on his holiday?  (1 mark)
  4. Bonn needs keep $600 for airfares to return home. With this in mind, what is the maximum number of weeks that Bonn can be on holidays?  (1 mark)
  5. Briefly describe what happens to the amount of savings as the number of weeks on holiday increases?  (1 mark)
Show Answers Only

a.    \(\text{Line graph}\)

b.    \(\text{Weeks on Holidays and Savings}\)

c.    \($300\)

d.    \(6\ \text{weeks}\)

e.    \(\text{As the number of weeks on holiday increases the amount of savings decreases.}\)

Show Worked Solution

a.    \(\text{Line graph}\)

b.    \(\text{Weeks on Holidays and Savings}\)

c.    \(\text{From the graph, the Savings spent per week}= $300\)

d.    \(\text{Maximum weeks on holidays}\)

\(=(2400-600)\ ÷\ 300\)

\(=6\ \text{weeks}\)

e.    \(\text{As the number of weeks on holiday increases the amount of savings decreases.}\)

Interpreting Data, SM-Bank 003

Margaret is preparing a report for her supervisor regarding costs for the recent staff development day.

Below is the graph Margaret prepared summarising the cost of the staff lunch for the day.

  1. What type of graph has been used to display the information?  (1 mark)
  2. Identify the two variables Margaret has used in this graph?  (1 mark)
  3. What is the cost of lunch per attendee?  (1 mark)
  4. If the total cost for the staff lunch was $85, how many attendees were there?  (1 mark)
  5. Briefly describe what happens to the total cost of the staff lunch as the number of attendees increases?  (1 mark)
Show Answers Only

a.    \(\text{Line graph}\)

b.    \(\text{Number of Attendees and Cost}\)

c.    \($5\)

d.    \(17\)

e.    \(\text{As the number of attendees increases the cost increases.}\)

Show Worked Solution

a.    \(\text{Line graph}\)

b.    \(\text{Number of Attendees and Cost}\)

c.    \(\text{From the graph, the cost per attendee}= $5\)

d.    \(\text{Number of Attendees}\)

\(=$85\ ÷\ 5\)

\(=17\)

e.    \(\text{As the number of attendees increases the cost increases.}\)