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Probability, SM-Bank 031

A car dealership contains 12 black, 8 red, 10 blue, 16 silver and 4 white cars.

Walter wears a blindfold and chooses one car at random.

What is the chance that the car is blue?  (2 marks)

Show Answers Only

\(\dfrac{1}{5}\)

Show Worked Solution
\(P\text{(Blue car)}\) \(=\dfrac{\text{number of blue cars}}{\text{total number of cars}}\)
  \(=\dfrac{10}{50}\)
  \(=\dfrac{1}{5}\)

Probability, SM-Bank 030

Luigi spins these two arrows. He then adds the numbers in the sections where the  arrows stop to get the total score.
 

 
How many different ways can Luigi get a total of 7?  (2 marks)

Show Answers Only

\(3\)

Show Worked Solution

\(\text{Consider the possibile ways to get 7}\)
 

 
 

\(\therefore\ \text{There are 3 ways to get a total of 7.}\)

Probability, SM-Bank 029 MC

Spiro spins the arrow of this spinner 40 times.

He records the number of times the arrow lands on each number.
 


 

Which table records the most likely results?

A.
B.
C.
D.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Landing on 1 or 5 is approximately one-third chance}\)

\(\text{which is approximately 13 times.}\)

\(\text{Landing on 4 is expected to occur slightly less often}\)

\(\text{than landing on 2 or 3.}\)

 \(\Rightarrow D\)

Probability, SM-Bank 028

Peter has a marble bag that contains 20 marbles that are either red or green in colour.

The probability of randomly picking a green marble is 70%.

  1. What is the probability of randomly picking a red marble?  (1 mark)
  2. How many red marbles are in the bag?  (1 mark)
Show Answers Only

a.    \(30\%\)

b.    \(6\)

Show Worked Solution
a.    \(P\text{(green)} + P\text{(red)}\) \(=100\%\)
\(70\% + P\text{(red)}\) \(=100\%\)
\(\therefore\ P\text{(red)}\) \(=30\%\)

 

b.    \(\text{Red marbles}\) \(=20\times 30\%\)
  \(=20\times \dfrac{3}{10}\)
  \(=6\)

Probability, SM-Bank 027 MC

Ryan has white and black marbles in his bag.

If he chooses a marble from the bag without looking he is likely, but not certain, to get a white marble.

Which is Ryan's bag?
 

A. B. C. D.

​

Show Answers Only

\(A\)

Show Worked Solution

\(\text{The 1st option gives a}\ \dfrac{3}{5}\ \text{chance of a}\)

\(\text{white marble (likely but not certain).}\)
 

\(\Rightarrow A\)

Probability, SM-Bank 026

Shirley uses this net to make a dice.

She rolls the dice once.

What is the chance that Shirley will roll a 2?  Give your answer in simplest fraction form.  (2 marks)

Show Answers Only

\(\dfrac{1}{3}\)

Show Worked Solution
\(P(2)\) \(=\dfrac{\text{Number of 2’s}}{\text{Total possibilities}}\)
  \(=\dfrac{2}{6}\)
  \(=\dfrac{1}{3}\)

Probability, SM-Bank 025 MC

Shane rolls a standard 6-sided dice once.

Which of the following is Shane most likely to roll?

  1. a number less than 3
  2. a number greater than 2
  3. an even number
  4. the number 3 or 4
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Consider the probability of each option:}\)

\(P\text{(a number less than 3)} =\dfrac{2}{6}\)

\(P\text{(a number greater than 2)} =\dfrac{4}{6}\)

\(P\text{(an even number)} =\dfrac{3}{6}=\dfrac{1}{2}\)

\(P\text{(3 or 4)} =\dfrac{2}{6}\)
 

\(\therefore\ \text{A number greater than 2 is most likely.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 023

Claudia gets to ring the school bell once every 5 school days.

Today is a school day.

What is the probability that Claudia will ring the school bell?

Show Answers Only

\(\dfrac{1}{5}\)

Show Worked Solution
\(P\text{(Claudia rings bell)}\) \(=\dfrac{\text{favorable events}}{\text{total possible events}}\)
  \(=\dfrac{1}{5}\)

Probability, SM-Bank 022

Bonny draws the number 1 or 2 on a group of discs, as pictured below.
 

 

 
One disc is chosen at random.

What is the chance the disc has a 2 drawn on it?  (1 mark)

Show Answers Only

\(\dfrac{5}{18}\)

Show Worked Solution
\(P\text{(2)}\) \(=\dfrac{\text{Number of 2’s}}{\text{Total discs}}\)
  \(=\dfrac{5}{18}\)

Probability, SM-Bank 021 MC

There are 20 raffle tickets, numbered 1 to 20, in a box.

Three prizes are given away by choosing three tickets from the box. Each ticket can win only one prize.

The first ticket drawn is number 15 and it wins the third prize.

Which of the following is not possible?
 

  1. Second prize is won by number 2.
  2. First prize is won by a prime number.
  3. Second prize is an even number.
  4. First prize is won by number 15.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{“First prize is won by number 15” is impossible because}\)

\(\text{number 15 has already been chosen and won 3rd prize.}\)

\(\text{(Note that there is no replacement of tickets.)}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 020

Jenny and Sam play a board game with the spinner shown.
 

 Jenny spins the arrow.

  1. On which number is the arrow most likely to stop?  (1 mark)
  2. What is the probability that Jenny spins a 3?  (1 mark)
  3. What is the probability that Jenny does NOT spin a 3?  (1 mark)
Show Answers Only

a.    \(3\)

b.    \(\dfrac{4}{9}\)

c.    \(\dfrac{5}{9}\)

Show Worked Solution

a.    \(\text{There are more 3’s than any other number.}\)

\(\therefore\ \text{Most likely to land on 3.}\)

b.    \(P\text{(3)}\) \(=\dfrac{\text{Number of 3’s}}{\text{Total divisions on spinner}}\)
    \(=\dfrac{4}{9}\)

 

c.    \(P\text{(not 3)}\) \(=1-P\text{(3)}\)
    \(=1-\dfrac{4}{9}\)
    \(=\dfrac{5}{9}\)

Probability, SM-Bank 019 MC

A spinner is spun once.
 

 

 
Each shape on the wheel has an equal chance.

What is the chance that the spinner lands on the triangle .
 

  1. 5 chances in 6
  2. 6 chances in 6
  3. 1 chance in 5
  4. 1 chance in 6
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Since all shapes have an equal chance,}\)

\(P\text{(triangle)}=\dfrac{1}{6}\)
 

\(\Rightarrow D\)

Probability, SM-Bank 018 MC

Kip spins the arrow on two identical spinners.

The arrow on each spinner is equally likely to land on 1, 2 or 3.
 

 
If Kip adds up the two results, which total is he least likely to get?

  1. 3
  2. 4
  3. 5
  4. 6
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Possible combinations:}\)

\((1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)\)

\(\text{A total of 6 only occurs once, (3 , 3) }\)

\(\text{so is the less likely to occur than 3, 4 or 5.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 017 MC

Dennis is a fast bowler. In a cricket game, the chance of him getting a wicket on a given ball is unlikely.

Which probability best describes Dennis' chance of getting a wicket from one particular ball?
 

  1. \(\dfrac{14}{15}\)
  2. \(\dfrac{1}{2}\)
  3. \(1\)
  4. \(\dfrac{1}{15}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Unlikely means the probability is}\)

\(\text{close to zero.}\)

\(\therefore\ \dfrac{1}{15}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 016 MC

The Rural Fire Service issued a statement that the chance of bushfires on a given day was extremely likely.

Which probability below best describes the chance of bushfires?

  1. \(\dfrac{1}{9}\)
  2. \(\dfrac{8}{9}\)
  3. \(1\)
  4. \(\dfrac{9}{8}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Probability of  “extremely likely” is close to 1}\)

\(\text{(probability cannot > 1)}\)

\(\therefore\ \dfrac{8}{9}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 015 MC

In a high school, all the boys were asked their favourite sport and the top five results were put in the table below.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Sport} \rule[-1ex]{0pt}{0pt} & \textbf{Number of boys} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby League} \rule[-1ex]{0pt}{0pt} & \text{123} \\
\hline
\rule{0pt}{2.5ex} \text{Soccer} \rule[-1ex]{0pt}{0pt} & \text{117} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby Union} \rule[-1ex]{0pt}{0pt} & \text{108} \\
\hline
\rule{0pt}{2.5ex} \text{Swimming} \rule[-1ex]{0pt}{0pt} & \text{106} \\
\hline
\rule{0pt}{2.5ex} \text{AFL} \rule[-1ex]{0pt}{0pt} & \text{100} \\
\hline
\end{array}

Which of these statements is true of a boy who goes to the high school?

  1. His favourite sport is less likely to be soccer than AFL.
  2. His favourite sport is certain to be rugby league.
  3. His favourite sport is more likely to be rugby union than swimming.
  4. It is impossible that his favourite sport is golf.
Show Answers Only

\(C\)

Show Worked Solution

\(\text{“His favourite sport is more likely to be rugby union}\)

\(\text{than swimming” is the correct statement.}\)
 

\(\Rightarrow C\)

Probability, SM-Bank 014 MC

The weather report says there is 80% chance of rain tomorrow.

Which of these describes the chance of it raining tomorrow?

  1. impossible
  2. unlikely
  3. likely
  4. certain
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Anything over 50% chance has more likelihood of}\)

\(\text{happening than not. Anything that is certain to}\)

\(\text{happen must be 100% chance.}\)

\(\therefore\ \text{80% chance is “likely”.}\)

 
\(\Rightarrow C\)

Probability, SM-Bank 013 MC

Mick has a bag of marbles. His marbles are orange, white, blue and green.
 

 
Mick picks one marble from his bag.

Which of the following could be the probability that the marble he picks is green.

  1. \(\dfrac{13}{3}\)
  2. \(1.52\)
  3. \(\dfrac{3}{13}\)
  4. \(6\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Any probability must be between 0 and 1 inclusive.}\)

\(\therefore\ \text{Only possibility is }\dfrac{3}{13}\)

 
\(\Rightarrow C\)

Probability, SM-Bank 012 MC

Two identical spinners are spun at the same time and the two numbers they land on are added up.
 

 
Which total is most likely?

  1. 4
  2. 7
  3. 10
  4. 12
Show Answers Only

\(B\)

Show Worked Solution

\(\text{A total of 7 can be achieved in 6 different ways.}\)

\(\text{All other totals have less possible combinations.}\)

\(\therefore\ \text{a total of 7 is the most likely.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 011 MC

A small disc is thrown onto the grid pictured below.
 

The disc has an equal chance of landing in any square.

Which numbered square is the disc least likely to land in?

  1. 3
  2. 4
  3. 5
  4. All numbers are equally likely
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Only 1 square is numbered 4 (all other numbers}\)

\(\text{have 2 squares).}\)

\(\therefore\ \text{The disc is least likely to land on the number 4.}\)

   
\(\Rightarrow B\)

Probability, SM-Bank 010 MC

A spinning wheel has sections labelled with different numbers.
 
 

If the spinner has an equal chance of landing in each section, which of the numbers is the spinner most likely to land on?

  1. 1 or 3
  2. 1
  3. 2 or 4
  4. All of the numbers are equally likely
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Since the spinner is divided into 8 equal sections}\)

\(\text{and each number has 2 sections, all numbers}\)

\(\text{are equally likely.}\)

   
\(\Rightarrow D\)

Probability, SM-Bank 009 MC

The arrow pictured below is spun once: 

Which number is the spinner most likely to land on?

  1. 1
  2. 2
  3. 3
  4. Same chance for each number.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{The sections that are labelled with a 2 are}\)

\(\text{the largest when combined.}\)

\(\therefore\ \text{Spinner most likely to land on 2.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 008 MC

A standard deck of 52 cards is made up of four suits - Hearts, Diamonds, Clubs and Spades.

Each suit contains 13 cards that include an Ace, King, Queen and Jack, together with numbered cards from 2 to 10.

Lara has a standard deck of cards and without looking, picks a number 7 and returns it to the deck.

She repeats this three times and draws a number 7 each time.

If she draws a 4th card without looking, which of the following is true?
 

  1. She is certain to draw a number 7.
  2. She is more likely to draw a number 7 than a Spade.
  3. She is less likely to draw a number 7 than a Queen.
  4. She is more likely to draw a Heart than a number 7.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{There are 13 hearts in the deck}\)

\(\text{There are 13 spades in the deck}\)

\(\text{There are 4 7’s in the deck}\)

\(\text{There are 4 queens in the deck}\)
 

\(\text{Consider Option D}\ \rightarrow\ \text{There are more hearts than 7’s}\)

\(\therefore\ \text{She is more likely to draw a heart than a 7}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 007 MC

Eight buttons, numbered 1 to 8, are placed in a bag.

Robin picks three buttons out of the bag without looking.

Once chosen, a button is not put back into the bag.

The first button is number 2.

Which of the following cannot happen?

  1. The second button is even.
  2. The third button is 2.
  3. The second button is odd.
  4. The third button is 8.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Once number 2 is picked, it cannot be}\)

\(\text{picked again (no replacement).}\)

\(\therefore\ \text{The third button cannot be 2.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 006 MC

Shapes are drawn on the balls below and placed in a bag.
 

 

Billy reaches into the bag and takes out a ball without looking.

Which type of ball is he least likely to take out?

A.
B.
C.
D.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Counting the balls of each type:}\)

\(6\times\)
\(5\times\)
\(3\times\)
\(2\times\)

 

\(\therefore\ \text{Least likely is  }\)

\(\Rightarrow A\)

Probability, SM-Bank 005 MC

These identical numbered discs were in a bag.

Julio selected one disc.
 

 

What is the chance that the disc Julio selected had a number less than 10 on it?

  1. Unlikely
  2. Certain
  3. Impossible
  4. Even
Show Answers Only

\(B\)

Show Worked Solution

\(\text{All the discs have numbers less than ten.}\)

\(\text{Therefore, the chance of a number being selected

\(\text{that is less than 10 is certain.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 004 MC

Which of the following spinners is the least likely to land on the coloured area?
A. B.

C. D.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{This spinner has the least area painted therefore}\)

\(\text{has the least chance of landing on a coloured}\)

\(\text{portion of the spinner.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 003 MC

Which of the following spinners will most likely land on the coloured area?
A. B.

C. D.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{This spinner has the most area painted therefore}\)

\(\text{has the highest chance of landing on a coloured}\)

\(\text{portion of the spinner.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 002 MC

A statistic shows that on a certain highway the chance of an accident happening on any day is 5%.

Which of the following describes the chance of having an accident today?

  1. Likely
  2. Certain
  3. Impossible
  4. Unlikely
Show Answers Only

\(D\)

Show Worked Solution

\(\text{An event with 100% chance of occurring is certain to happen.}\)

\(\text{The chance of an accident happening today is 5%.}\)

\(\therefore\ \text{It is unlikely to happen since the chance is very low.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 001 MC

These identical numbered discs were in a bag.

Gay selected one disc.
 


 

What is the chance that the disc Gay selected had a 7 on it?

  1. Unlikely
  2. Certain
  3. Impossible
  4. Even
Show Answers Only

\(C\)

Show Worked Solution

\(\text{The discs have the following numbers:}\)

\(\text{There are no discs with a 7}\)

\(\therefore\ \text{The chance the selected disc has a 7 on it is impossible.}\)

 
\(\Rightarrow C\)

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

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

\(=91.66\dots\)

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

Data Analysis, SM-Bank 056 MC

The dot plot below shows the times, in seconds, of 40 runners in the qualifying heats of their 800 m club championship.
 

The shape of this distribution is best described as

  1. positively skewed with one outlier.
  2. approximately symmetric with one outlier.
  3. approximately symmetric with no outliers.
  4. negatively skewed with one outlier.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Distribution is positively skewed (tail stretches to the right)} \)

\(\text{and 146 is a possible outlier}\)

\(\Rightarrow A\)

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 005

While packaging cookies for the Easter show, Johnny recorded the number of broken cookies in each batch.

Broken cookies per batch

\(05\ ,\ 12\ ,\ 09\ ,\ 02\ ,\ 31\ ,\ 11\ ,\ 10\ ,\ 18\ ,\ 20\)

\(25\ ,\ 23\ ,\ 06\ ,\ 15\ ,\ 21\ ,\ 30\ ,\ 35\ ,\ 19\ ,\ 49\)

 

  1. Use the data to complete the stem-and-leaf plot below.  (1 mark)
     

  2. What is the range of broken cookies?  (1 mark)
  3. What is the median number of broken cookies?  (1 mark)
  4. Is the distribution symmetrical, positively skewed or negatively skewed?  (1 mark)
Show Answers Only

a.

b.    \(47\)

c.    \(18.5\)

d.    \(\text{Positively skewed}\)

Show Worked Solution

a.

b.    \(\text{Range} = 49-2=47\)

c.    \(\text{18 scores → Median}\)

\(=\dfrac{\text{9th + 10th}}{2}\)

\(=\dfrac{18+19}{2}=18.5\)

d.    \(\text{Positively skewed}\)

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