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Displaying Data, SM-Bank 043

While working at the Year 7 camp, Gene counted how many bullseyes the archery group achieved during the afternoon activity.

He summarised the data in the table below.
  

\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Number of Bullseyes} \rule[-1ex]{0pt}{0pt} & \  0\   &  \  1\   & \  2\   & \  3\   & \  4\   & \  5\   & \  6  \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} &7 &5&3&5&2&2&1 \\
\hline
\end{array}

  1. How many students were in the afternoon session of archery?  (1 mark)
  2. How many students scored zero bullseyes?  (1 mark)
  3. Assuming all shots were bullseye attempts, how many shots at the bullseye were made?  (1 mark)
  4. Display this data in a vertical column graph using the grid below.  (2 marks)
     

Show Answers Only

a.    \(25\)

b.    \(7\)

c.    \(57\)

d.   

Show Worked Solution

a.    \(\text{Number of students} = 25\)

b.    \(\text{Zero bullseyes} = 7\)

c.   
\(\text{Total shots at bullseye}\) \(=7+5\times 1+3\times 2+5\times 3+2\times 4+2\times 5+1\times 6\)
    \(=57\)

\(\text{NOTE:  The question asks for total shots NOT total value of shots,}\)

\(\text{therefore, the 7 who score 0 bullseyes must be added in.}\)

d.

Displaying Data, SM-Bank 042

The marks below were recorded by Ms Smith for her students in a recent statistics quiz. The highest possible score was 5.
 

\(3,\ 1,\ 5,\ 2,\ 1,\ 3,\ 4,\ 1,\ 4,\ 2,\ 4,\ 5,\ 3,\ 4,\ 2,\ 4,\ 3,\ 0,\ 5,\ 1,\ 4\)
 

  1. Summarise the data using the table below.  (1 mark)
    \begin{array} {|l|c|c|c|c||}
    \hline
    \rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & \  0\   &  \  1\   & \  2\   & \  3\   & \  4\   & \  5\   \\
    \hline
    \rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & &&&&& \\
    \hline
    \end{array}

  2. Represent this data as a column graph using the grid below.  (2 marks)
     

     
  3. How many students sat for the quiz?  (1 mark)
  4. If the pass mark was 60%, how many students passed the quiz?  ( 1 mark)
  5. What was the average score achieved in the quiz? Give your answer correct to one decimal place.  (1 mark)
Show Answers Only

a.

\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & 0&1&2&3&4&5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & 1&4&3&4&6&3 \\
\hline
\end{array}

b.   

c.    \(21\)

d.    \(13\)

e.    \(2.9\)

Show Worked Solution

a.

\begin{array} {|l|c|c|c|c||}
\hline
\rule{0pt}{2.5ex} \textbf{Score} \rule[-1ex]{0pt}{0pt} & 0&1&2&3&4&5 \\
\hline
\rule{0pt}{2.5ex} \textbf{Number of Students} \rule[-1ex]{0pt}{0pt} & 1&4&3&4&6&3 \\
\hline
\end{array}

b.   


 

c.    \(21\)

 

d.    \(60\%\ \text{pass mark}\) \(=5\times \dfrac{60}{100}\)
    \(=3\)

 
\(\therefore\ 4+6+3 = 13\ \text{students passed the quiz}\)

 

e.    \(\text{Average score}\) \(=\dfrac{1\times 0+4\times 1+3\times 2+4\times 3+6\times 4+3\times 5}{21}\)
    \(=\dfrac{61}{21}\)
    \(=2.904\dots\approx 2.9\ \text{(1 d.p.)}\)

Displaying Data, SM-Bank 041

Stuart collected the eggs from his free range chickens and recorded the number of eggs he collected each day for two weeks.
 

\(3,\ 1,\ 5,\ 5,\ 1,\ 3,\ 4,\ 1,\ 4,\ 1,\ 4,\ 5,\ 1,\ 4\)
 

  1. Represent this data as a dot plot using the grid below.  (2 marks)
     

  2. How many eggs were collected altogether?  ( 1 mark)
  3. What is the average number of eggs Stuart collected?  (1 mark)
Show Answers Only

a.

b.    \(42\)  

c.    \(3\)

Show Worked Solution

a.

 
 

b.    \(\text{Total eggs}\) \(=5\times 1+2\times 3+4\times 4+3\times 5\)
    \(=42\)

 

c.    \(\text{Average number of eggs}\) \(=\dfrac{42}{14}\)
    \(=3\)

Displaying Data, SM-Bank 040

The heights, in centimetres, of David's hockey side are as follows:
 

\(172,\ 177,\ 171,\ 174,\ 174,\ 176,\ 173,\ 177,\ 174,\ 172,\ 174\)
 

  1. Represent this data as a dot plot using the grid below.  (2 marks)
     

  2. What is the average height of the players in David's hockey team?  (2 marks)
Show Answers Only

a.

b.    \(174\ \text{cm}\)

Show Worked Solution

a.


 

b.    \(\text{Average height}\) \(=\dfrac{171+2\times 172+173+4\times 174+176+2\times 177}{11}\)
    \(=\dfrac{1914}{11}\)
    \(=174\ \text{cm}\)

Displaying Data, SM-Bank 035

The graph below shows the favourite subjects of a group of 100 students.

 

   
  1. How many students in total chose either Technology or English as their favourite subject?  (1 mark)

  2. What percentage of students preferred either Science or PDHPE?  (2 marks)

  3. How many more students chose Maths as their favourite subject than History?  (1 mark)

Show Answers Only

a.    \(23\ \text{students}\)

b.    \(31\%\)

c.    \(10\ \text{students}\)

Show Worked Solution
a.     \(\text{Technology or English}\) \(=10+13\)
    \(=23\ \text{students}\)

 

b.     \(\text{Percentage Science or PDHPE}\) \(=\dfrac{16+15}{100}\times 100%\)
    \(=31\%\)

 

c.     \(\text{Difference}\) \(=19-9\)
    \(=10\ \text{students}\)

Displaying Data, SM-Bank 034

The graph below shows the outdoor activities chosen by students at the Year 7 camp.

 

 
  1. How many students in total chose either high ropes or abseiling?  (1 mark)

  2. What was the average number of students participating in each of the activities? Give your answer correct to the nearest whole number.  (2 marks)

  3. How many more students chose the Giant Swing than Hiking? (1 mark)

Show Answers Only

a.   \(21\ \text{students}\)

b.   \(14\ \text{students (nearest whole number)}\)

c.    \(9\ \text{students}\)

Show Worked Solution
a.     \(\text{High ropes and abseiling}\) \(=9+12\)
    \(=21\ \text{students}\)

 

b.     \(\text{Average students/activity}\) \(=\dfrac{15+12+24+9+7+19}{6}\)
    \(=\dfrac{86}{6}\)
    \(=14.333\dots\)
    \(=14\ \text{students (nearest whole number)}\)

 

c.     \(\text{Difference}\) \(=24-15\)
    \(=9\ \text{students}\)

Displaying Data, SM-Bank 033

The graph below shows the times Kerry spent, in minutes, performing different exercises at the gym over the last fortnight.

 

 
  1. How many minutes in total did Kerry spend cycling and walking? (1 mark)

  2. What was the average time per day that Kerry spent exercising over the last fortnight? Give your answer correct to the nearest minute.  (2 marks)

  3. How many more minutes did Kerry spend doing HIIT than rowing?  (1 mark)

Show Answers Only

a.   \(\text{150 minutes}\)

b.   \(28\text{ minutes (nearest minute)}\)

c.    \(35\text{ minutes}\)

Show Worked Solution
a.     \(\text{Cycling and walking}\) \(=90+60\)
    \(=150\ \text{minutes}\)

 

b.     \(\text{Average exercise minutes/day}\) \(=\dfrac{60+45+90+40+75+80}{14}\)
    \(=\dfrac{390}{14}\)
    \(=27.857\dots\)
    \(=28\text{ minutes (nearest minute)}\)

 

c.     \(\text{Difference}\) \(=75-40\)
    \(=35\ \text{minutes}\)

Displaying Data, SM-Bank 032

The graph below shows the depth of water in a sea bath from 6.00 am to 8.00 pm.
 

 

  1. What was the maximum depth, in metres, of water in the sea bath?  (1 mark)

  2. The sea bath was open to the public when the depth of water was above 1.5 m.

     

    Between which times was the sea bath open?  (1 mark)


Show Answers Only

a.   \(\text{2 metres}\)

b.   \(\text{8 am – 6 pm}\)

Show Worked Solution

a.   \(\text{2 metres}\)

b.   \(\text{8 am – 6 pm}\)

Displaying Data, SM-Bank 031

  1. Draw an ordered stem-and-leaf plot for the following set of scores.
     
    \(51\ \ \ \ \ 56\ \ \ \ \ 58\ \ \ \ \ 36\ \ \ \ \ 28\ \ \ \ \ 45\ \ \ \ \ 53\ \ \ \ \ 69\ \ \ \ \ 47\ \ \ \ \ 52\)     (2 marks)

  2. What is the median of the set of scores?   (1 mark)

  3. Comment on the skewness of the set of scores.   (1 mark)

Show Answers Only
a.    \begin{array} {r|lll} \textbf{Stem} & \textbf{Leaf} \\ \hline 2 & 8 \\ 3 & 6 \ \\ 4 & 5\ 7\\ 5 & 1\ 2\ 3\ 6 \ 8 \\ 6 & 9 \\ \end{array}

b.    \(51.5\)

c.    \(\text{The data has a tail that stretches to the left}\)

\(\therefore\ \text{Data is negatively skewed.}\)

Show Worked Solution
a.    \begin{array} {r|lll} \textbf{Stem} & \textbf{Leaf} \\ \hline 2 & 8 \\ 3 & 6 \ \\ 4 & 5\ 7\\ 5 & 1\ 2\ 3\ 6 \ 8 \\ 6 & 9 \\ \end{array}

 

b.    \(\text{10 scores}\)

\(\therefore\ \text{Median}\) \(=\dfrac{\text{(5th + 6th)}}{2}\)
  \(=\dfrac{51 + 52}{2}\)
  \(=51.5\)

 

c.    \(\text{The data has a tail that stretches to the left}\)

\(\therefore\ \text{Data is negatively skewed.}\)

Displaying Data, SM-Bank 030

A random sample of people were asked what is their favourite winter sport.

The table below recorded the results.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Sport} \rule[-1ex]{0pt}{0pt} & \textbf{Number of People} \\
\hline
\rule{0pt}{2.5ex} \text{Netball} \rule[-1ex]{0pt}{0pt} & \text{25} \\
\hline
\rule{0pt}{2.5ex} \text{Aussie Rules} \rule[-1ex]{0pt}{0pt} & \text{35} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby League} \rule[-1ex]{0pt}{0pt} & \text{30} \\
\hline
\rule{0pt}{2.5ex} \text{Ice Hockey} \rule[-1ex]{0pt}{0pt} & \text{10} \\
\hline
\end{array}

  1. Use the information in the table to construct a divided bar graph on the template below. Remember to include a title and labels.  (2 marks)
     

     
  2. Using the data from the survey, predict how many people would choose Aussie Rules if 2000 people were surveyed. (2 marks)
Show Answers Only

a. 

b.    \(700\)

Show Worked Solution
 

a.    \(\text{Total Number Sampled}\) \(=25+35+30+10\)
    \(=100\)

 
\(\text{Division on the template}=\dfrac{100}{20}=5\ \text{people}\)

b.    \(\text{Aussie rules}\) \(=\dfrac{35}{100}\times 2000\)
    \(=700\)

 
\(\therefore\ \text{700 people would be predicted to choose Aussie Rules}\)

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

Displaying Data, SM-Bank 028

Melinda and Cathy run the 100 metre sprint in their school athletics carnival.

A device tracks their progress and the results are shown in separate line graphs below.
 

 
Melinda starts quickly and passes the 75 metre mark after 10 seconds, slowing down as the race progresses.

Cathy is slower but runs the whole race at the same speed.

Approximately how long after Melinda did Cathy pass the 75 metre mark in the race?  (2 marks)

Show Answers Only

\(5\ \text{seconds}\)

Show Worked Solution

\(\text{Melinda passes 75 metre mark at 10 seconds.}\)

\(\text{Cathy passes at approximately 15 seconds.}\)

\(\therefore\ \text{Cathy passes approximately 5 seconds after Melinda.}\)

Displaying Data, SM-Bank 027

This graph shows the UV index for the town of Coonamble during one day.
 

 
Between which hours was the UV index always in the high range?  (1 mark)

​

Show Answers Only

\(\text{11 am – 12 pm, 2 pm – 3 pm}\)

Show Worked Solution

\(\text{UV index is on high:}\)

\(\text{between 11 am – 12 pm and between 2 pm – 3 pm}\)

Displaying Data, SM-Bank 026

Tom collected data on the number of big game animals in an African wildlife park.

This graph shows how many big game animals lived in the park.

 

 

There were 16 more elephants than rhinos in the wildlife park.

  1. What fraction of the animals were elephants?  (1 mark)
  2. What fraction of the animals were rhinos?  (1 mark)
  3. How many big game animals were in the park in total?  (2 marks)

Show Answers Only

a.    \(\dfrac{7}{20}\)

b.    \(\dfrac{3}{20}\)

c.    \(80\)

Show Worked Solution

a.    \(\text{There are 20 divisions on the sector graph}\)

\(\text{Elephants}=\dfrac{7}{20}\)

b.    \(\text{Rhinos}=\dfrac{3}{20}\)

c.    \(\text{Let}\ \ n =\ \text{total big games animals in the park}\)

\(\text{Elephants – Rhinos}\) \(=16\)
\(\dfrac{7}{20} n-\dfrac{3}{20}n\) \(=16\)
\(\dfrac{4}{20}n\) \(=16\)
\(n\) \(=\dfrac{16\times 20}{4}\)
  \(= 80\)

 
\(\therefore\ \text{There are 80 big game animals in the park}\)

Displaying Data, SM-Bank 025

Bradley's class were asked to choose their favourite colour among four choices.

  • 5 voted for red which represented 90° on the sector graph
  • 2 voted for orange
  • 6 voted for blue
  • The rest voted for green

 

 

How many students in Bradley's class chose green?  (2 marks)

Show Answers Only

`7`

Show Worked Solution

\(\text{Since red is 90° it is one-quarter of the sector graph}\)

\(\rightarrow\ \text{There are 20 students in Bradley’s class.}\)

\(\therefore\ \text{Votes for green}\)

\(=20-(5+2+6)\)

\(=7\)

Displaying Data, SM-Bank 024

Kat went on her annual holiday and spent her money on accommodation, meals and shopping.

She spent $1200 in total and the pie chart below shows how she spent it.

 
 

  1. How much money did Kat spend on shopping?  (2 marks)
  2. How much money did Kat spend on meals?  (2 marks)
Show Answers Only

a.    \($396\)

b.    \($264\)

Show Worked Solution

a.    \(\text{Money spent on shopping}\)

\(=33\%\times 1200\)

\(=$396\)

 
b.    \(\text{Money spent on meals}\)

\(=1200-(540+396)\)

\(=$264\)

Displaying Data, SM-Bank 023 MC

A survey was conducted that asked students how long it took them to travel to school. This graph show the results.
 


 

What percentage of students had a commute between \(15-30\) minutes?

  1. less that 25%
  2. between 25% and 50%
  3. between 50% and 75%
  4. more than 75%
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Section (15 – 30 minutes) is more than one quarter}\)

\(\text{of the chart and less than half.}\)

\(\therefore\ \text{between 25% and 50%}\)
 

\(\Rightarrow B\)

Displaying Data, SM-Bank 021 MC

Anne taught a kindergarten class and asked her students what their favorite fruit is.

Their answers were used to draw the pie chart below.
 

 

 
Around a quarter of her students preferred which fruit?

  1. Banana
  2. Apple
  3. Mango
  4. Grapes
Show Answers Only

\(B\)

Show Worked Solution

\(\text{A quarter of students will represent a sector that}\)

\(\text{is the size of a quarter of the circle }\rightarrow\ \text{Apple}\) 
 

\(\Rightarrow B\)

Displaying Data, SM-Bank 020 MC

A store sells second hand mobile phones.

The graph below shows the price of 2 similar second-hand phones.
 

 

Which of the following is true based on the graph shown?

  1. Phone A is older and less expensive than Phone B
  2. Phone B is older and more expensive than phone A
  3. Phone A is newer and more expensive than Phone B
  4. Phone A is older and more expensive than Phone B

Show Answers Only

\(C\)

Show Worked Solution

\(\text{Phone A is left of Phone B }\rightarrow\ \text{ it is newer.}\)

\(\text{Phone A is higher than Phone B }\rightarrow\ \text{it is more expensive.}\)
 

\(\therefore\ \text{Phone A is newer and more expensive than Phone B.}\)
 

\(\Rightarrow C\)

Displaying Data, SM-Bank 019 MC

Christie 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 a.m.} \rule[-1ex]{0pt}{0pt} & \text{9 a.m.} \rule[-1ex]{0pt}{0pt} & \text{12 p.m.} \rule[-1ex]{0pt}{0pt} & \text{3 p.m.} \\
\hline
\rule{0pt}{2.5ex} \text{Temperature (°C)} \rule[-1ex]{0pt}{0pt} & \text{22} \rule[-1ex]{0pt}{0pt} & \text{27} \rule[-1ex]{0pt}{0pt} & \text{32} \rule[-1ex]{0pt}{0pt} & \text{26} \\
\hline
\end{array}

 
Which graph shows Christie's results?
 

A.   B.
 
C.   D.
 
Show Answers Only

\(B\)

Show Worked Solution

\(\text{1st increase } = 27-22 = 5^{\circ}\)

\(\text{2nd increase } = 32-27 = 5^{\circ}\)
 

\(\longrightarrow\ \text{Temperature then drops 6° to 26°}\)
 

\(\Rightarrow B\)

Displaying Data, SM-Bank 018 MC

Natalie is the supervisor of the Maths club and keeps a record of the number of students in the club at the end of each week.
 

 
If no students have left the club, how many joined in Week 3?

  1. 5
  2. 7
  3. 9
  4. 21
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Students in club:}\)

\(\text{At the end of week 2 = 16}\)

\(\text{At the end of week 3 = 21}\)

\(\therefore\ \text{Students who joined in week 3}\)

\(=21-16\)

\(=5\)

\(\Rightarrow A\)

Displaying Data, SM-Bank 017 MC

Mathew is captain of the drama club and keeps a record of the number of students in the club at the end of each week.
 

 
If no students have left the club, how many joined in Week 3?

  1. 3
  2. 8
  3. 11
  4. 33
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Students in club:}\)

\(\text{At the end of week 2 = 22}\)

\(\text{At the end of week 3 = 33}\)

\(\therefore\ \text{Students who joined in week 3}\)

\(=33-22\)

\(=11\)

\(\Rightarrow C\)

Displaying Data, SM-Bank 016

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

Simon scored 6 goals in the season.

Gigi scored 3 goals.

How many more goals did Henry score than Fiona?  (2 marks)

Show Answers Only

\(7\ \text{goals}\)

Show Worked Solution

\(\text{Since Simon scored 6 goals}\)

\(\longrightarrow\ \text{1 soccer ball = 2 goals}\)

\(\longrightarrow\ \text{Henry scored 8 goals.}\)

\(\longrightarrow\ \text{Fiona scored 1 goals.}\)
 

\(\therefore\ \text{Extra goals}\) \(=8-1\)
  \(=7\ \text{goals}\)

Displaying Data, SM-Bank 015

The picture graph shows how many tonnes of concrete are needed for 4 jobs.
 

 
How many more tonnes of concrete does Job 1 need than Job 3?  (2 marks)

Show Answers Only

\(2\ \text{tonnes}\)

Show Worked Solution

\(\text{Job 1 needs 9 tonnes}\)

\(\text{Job 2 needs 7 tonnes}\)
 

\(\therefore\ \text{Extra tonnes}\) \(=9-7\)
  \(=2\ \text{tonnes}\)

Displaying Data, SM-Bank 014 MC

The bottles in Leisa's fridge are pictured below.
 

 
Leisa decides to make a graph where each bar represents one type of bottle in her fridge.
 

 
Leisa makes an error when creating the graph.

What should Leisa do to correct the error?

  1. Change the 'Number of bottles' label to 'Volume of bottles'.
  2. Change the title to 'Number of bottles in the fridge by volume'.
  3. The thickness of each bar should vary, depending on the number of bottles.
  4. Remove the 'Water' category since tonic water and soda water are already shown.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Remove the ‘Water’ category since tonic water and}\)

\(\text{soda water are already shown.}\)

\(\Rightarrow D\)

Displaying Data, SM-Bank 013 MC

Patrick counts the number of moths he has collected.

  • 9 Bogon moths
  • 3 Atlas moths
  • 6 Gypsy moths

In each picture graph below,  = 3 moths

Select the picture graph that shows the number of moths Patrick counts.

A.   B.
 
C.   D.
 
Show Answers Only

\(A\)

Show Worked Solution
  \(\text{= 3 moths}\)
    \(\text{= 6 moths}\)
     \(\text{= 9 moths}\)

 

\(\Rightarrow A\)

Displaying Data, SM-Bank 012 MC

During picking season, four groups of people were hired to pick apples.

A group will receive a bonus if they pick more than 24 apples per person in a 10-minute period.

The table below shows the total amount of apples picked by each group in the first 10 minutes.
 

 
Which group would have received a bonus in the first 10-minute period?

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

\(C\)

Show Worked Solution

\(\text{Calculate apples picked per person (in 10 mins) for each group:}\)

\(\text{A} = 68\ ÷\ 3=22.67\dots\)

\(\text{B} = 95\ ÷\ 4 = 23.75\)

\(\text{C} = 122\ ÷\ 5 = 24.4\)

\(\text{D} = 143\ ÷\ 6 = 23.83\dots\)
 

\(\Rightarrow C\)

Displaying Data, SM-Bank 011 MC

Chris did a survey of the number of female toilets in four shopping centres.

The results were recorded in the table below but the key has been left off the graph?

The total number of female toilets was 44.

How many toilets does represent in the graph?
  1. 1
  2. 2
  3. 4
  4. 5
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Total number of female symbols}\)

\(=5+4.5+5.5+7\)

\(=22\)
 

\(\therefore\ \text{The number of toilets one symbol represents}\)

\(=\dfrac{44}{22}\)

\(=2\)

 
\(\Rightarrow B\)

Displaying Data, SM-Bank 010 MC

Each bar on this graph shows the population of a country and the population of its capital city.

The white section is the population that lives in the capital city.

The black section is the population that lives outside the capital city.
 

   
 

Which of the following countries has the highest percentage of its population living in its capital city?

  1. Australia
  2. Belgium
  3. France
  4. England
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Considering the length of the white section of each}\)

\(\text{bar and comparing it to the length of the total bar,}\)

\(\text{Belgium easily has the highest percentage living in}\)

\(\text{its capital city.}\)

\(\Rightarrow B\)

Displaying Data, SM-Bank 009

Angus asked all the students in his primary school how far away they lived from school.

He used the results to create the column graph below but left off some labels.
 

 
Angus' primary school has 100 students.

How many students lived over 8 km from school?  (2 marks)

Show Answers Only

\(18\ \text{students}\)

Show Worked Solution

\(\text{Since there are 5 columns and 100 students, the }\)

\(\text{average number of students per column is 20.}\)
 

\(\longrightarrow\ \text{Each interval = 4 students}\)
 

\(\therefore\ \text{Number of students living over 8 km away}\)

\(=4.5\times 4\)

\(=18\ \text{students}\)

Displaying Data, SM-Bank 008

Two fishing boats record the number of tuna they catch on four fishing trips.
 

 
How many more tuna did Boat 2 catch than Boat 1 in total over the four trips.  (2 marks)

Show Answers Only

\(60\)

Show Worked Solution
\(\text{Boat 1 tuna}\) \(=140+120+40+55\)
  \(=355\)

 

\(\text{Boat 2 tuna}\) \(=105+130+95+85\)
  \(=415\)

 
\(\therefore\ \text{Extra tuna caught by Boat 2}\)

\(=415-355\)

\(=60\)

Displaying Data, SM-Bank 007 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. 45
  4. 60
Show Answers Only

\(C\)

Show Worked Solution

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

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

\(\Rightarrow C\)

Displaying Data, SM-Bank 006 MC

This graph shows a company's profit over a four year period.
 

 
Which conclusion can be reached from the graph?

  1. The profit in Year 2 was double of the profit in Year 1.
  2. The profits were greater than $20 000 in the period between Year 1 and Year 4.
  3. The profit in Year 4 was one quarter the profit in Year 3.
  4. The profits were positive in Years 2 and 3, and negative in Years 1 and 4.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Important to note that profits in this table begin at }$25\ 000, \text{not zero.}\)

\(\therefore\ \text{Profits were greater than }$20\ 000 \text{ in the period}\)

\(\text{between Year 1 and Year 4.}\)

\(\Rightarrow B\)

Displaying Data, SM-Bank 005

Matt and Libby love nature and planted 50 trees each over 3 weeks.

The bar chart below shows the number of trees each of them 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

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

\(= 35-15\)

\(= 20\)

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

\(= 45-20\)

\(= 25\)
 

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

Displaying Data, SM-Bank 003 MC

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

 
Which statement is most accurate based on the graph?

  1. There are more utility vehicles than trucks and vans.
  2. Utility vehicles are the most common type of vehicles
  3. There are more Australian vehicles than European vehicles.
  4. There are more Asian vehicles than European vehicles.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Consider the 4th option:}\)

\(\text{Total Asian vehicles}\)

\(=5+7+7=19\)

\(\text{Total European vehicles}\)

\(=4+3+3=10\)

\(\therefore\ \text{There are more Asian vehicles than European vehicles.}\)

\(\Rightarrow D\)

Displaying Data, SM-Bank 002 MC

Clive and Alvin asked their friends how many books they had read in the past month.

Clive draws a picture graph to show the results for his friends.

Alvin draws a column graph to show the results for his friends.
 

 
How many more of Clive's friends read 3-4 books in the last month than Alvin's friends?

  1. 0
  2. 4
  3. 6
  4. 8
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Number of Clive’s friends}\)

\(=4\times 2\)

\(=8\)

\(\text{Number of Alvin’s friends}\)

\(=2\)

\(\therefore\ \text{6 more of Clive’s friends.}\)

\(\Rightarrow C\)

Statistics, STD2 S1 2005 HSC 24d

The sector graph shows the proportion of people, as a percentage, living in each region of Sumcity. There are 24 000 people living in the Eastern Suburbs.
 

2UG-2005-24d1
 

  1. Show that the total number of people living in Sumcity is  160 000.  (1 mark)

Jake used the information above to draw a column graph.
 

2UG-2005-24d2

  1. The column graph height is incorrect for one region.

     

    Identify this region and justify your answer.   (2 marks)

Show Answers Only
  1. `160\ 000`
  2. `text(Western Suburbs population)`
Show Worked Solution

i.   `text(Let the population of Sumcity =)\ P`

`text(15%)× P` `= 24\ 000`
`:.P`  `= (24\ 000)/0.15` 
  `= 160\ 000\ …\ text(as required)` 

 

ii.  `text(Western Suburbs population)`

`= text(10%) × 160\ 000`

`= 16\ 000`

`text(The column graph has this population as)`

`text(12 000 people which is incorrect.)`

Statistics, STD2 S1 2005 HSC 24a

  1. Draw a stem-and-leaf plot for the following set of scores.

  2.  

     

    `21\ \ \ 45\ \ \ 29\ \ \ 27\ \ \ 19\ \ \ 35\ \ \ 23\ \ \ 58\ \ \ 34\ \ \ 27`  (2 marks)

  3. What is the median of the set of scores?   (1 mark)

  4. Comment on the skewness of the set of scores.   (1 mark)

Show Answers Only
  1.  
  2. `28`
  3. `text(The data has a tail that stretches to the right)`

  4.  

    `:.\ text(Data is positively Skewed.)`

Show Worked Solution
i.    HSC 2005 24a

 

ii.  `text(10 scores)`

`:.\ text(Median)` `= text{(5th + 6th)}/2`
  `= (27 + 29)/2`
  `= 28`

 

iii.  `text(The data has a tail that stretches to the right)`

`:.\ text(Data is positively skewed.)`

Statistics, STD2 S1 2004 HSC 8 MC

This sector graph shows the distribution of 116 prizes won by three schools: X, Y and Z.
 

 
How many prizes were won by School X?

  1.   26
  2.   32
  3.   81
  4.   99
Show Answers Only

`B`

Show Worked Solution

`text(Centre angle of School X sector)`

`= 100^@\ text{(by measurement)}`
 

`:.\ text(Prizes won by school X)`

`= 100/360 xx 116`

`= 32.22\ …`

`=> B`

Statistics, STD2 S1 2008 HSC 23e

In a survey, 450 people were asked about their favourite takeaway food. The results are displayed in the bar graph.

2008 23e
 
How many people chose pizza as their favourite takeaway food?   (2 marks)

Show Answers Only

`175`

Show Worked Solution

`text(Number of people who chose pizza)`

COMMENT: This question required measurement of the actual image on the exam. The same methodology works here.

`= text{Length of pizza section}/text{Total length of bar} xx 450`

`~~ 7/18 xx 450`

`~~ 175`
 

`:.\ 175\ text(people chose pizza.)`

Statistics, STD2 S1 2011 HSC 25b

The graph below displays data collected at a school on the number of students
in each Year group, who own a mobile phone.
 

2UG 2011 25b
 

  1. Which Year group has the highest percentage of students with mobile phones? (1 mark)

  2. Two students are chosen at random, one from Year 9 and one from Year 10.

     

    Which student is more likely to own a mobile phone?

     

    Justify your answer with suitable calculations. (2 marks)

  3. Identify a trend in the data shown in the graph. (1 mark)

Show Answers Only
  1. `text{Year 12 (100%)}`
  2. `text(Year 10)`
  3. `text(See Worked Solutions for detail)`
Show Worked Solution

i.   `text(Year 12 (100%))`

MARKER’S COMMENT: Many students ignore the instruction to use calculations and lose marks as a result.
 

ii.     `text(% Ownership in Year 9)` `=55/70`
    `=\ text{78.6%  (1d.p.)}`
      `text(% Ownership in Year 10)` `=50/60`
    `=\ text{83.3%  (1d.p.)}`

  
`:.\ text(The Year 10 student is more likely to own a mobile phone.)`

 

iii.   `text(% Ownership increases as students)`

 `text(progress from Year 7 to Year 12.)`