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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 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 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 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 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 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 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 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.)`