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Data Analysis, GEN2 2023 VCAA 2a

The following data shows the sizes of a sample of 20 oysters rated as small, medium or large.

\begin{array} {ccccc}
\text{small} & \text{small} & \text{large} & \text{medium} & \text{medium} \\
\text{medium} & \text{large} & \text{small} & \text{medium} & \text{medium}\\
\text{small} & \text{medium} & \text{small} & \text{small} & \text{medium}\\
\text{medium} & \text{medium} & \text{medium} & \text{small} & \text{large}
\end{array}

  1. Use the data above to complete the following frequency table.   (1 mark)

  1. Use the percentages in the table to construct a percentage segmented bar chart below. A key has been provided.   (1 mark)

     

Show Answers Only

i.    

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Size} \rule[-1ex]{0pt}{0pt} & \textbf{Number} & \textbf{Percentage (%) } \\
\hline
\rule{0pt}{2.5ex} \text{small} \rule[-1ex]{0pt}{0pt} & 7 & 35 \\
\hline
\rule{0pt}{2.5ex} \text{medium} \rule[-1ex]{0pt}{0pt} & 10 & 50 \\
\hline
\rule{0pt}{2.5ex} \text{large} \rule[-1ex]{0pt}{0pt} & 3 & 15 \\
\hline
\rule{0pt}{2.5ex} \textbf{Total} \rule[-1ex]{0pt}{0pt} & 20 & 100 \\
\hline
\end{array}

ii.    
     

Show Worked Solution

i.    

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Size} \rule[-1ex]{0pt}{0pt} & \textbf{Number} & \textbf{Percentage (%) } \\
\hline
\rule{0pt}{2.5ex} \text{small} \rule[-1ex]{0pt}{0pt} & 7 & 35 \\
\hline
\rule{0pt}{2.5ex} \text{medium} \rule[-1ex]{0pt}{0pt} & 10 & 50 \\
\hline
\rule{0pt}{2.5ex} \text{large} \rule[-1ex]{0pt}{0pt} & 3 & 15 \\
\hline
\rule{0pt}{2.5ex} \textbf{Total} \rule[-1ex]{0pt}{0pt} & 20 & 100 \\
\hline
\end{array}

 
ii.    
         

CORE, FUR1 2021 VCAA 1-3 MC

The percentaged segmented bar chart below shows the age (under 55 years, 55 years and over) of visitors at a travel convention, segmented by preferred travel destination (domestic, international).
 

Part 1

The variables age (under 55 years, 55 years and over) and preferred travel destination (domestic, international) are

  1. both categorial variables.
  2. both numerical variables.
  3. a numerical variable and a categorical variable respectively.
  4. a categorical variable and a numerical variable respectively.
  5. a discrete variable and a continuous variable respectively.

 
Part 2

The data displayed in the percentaged segmented bar chart supports the contention that there is an association between preferred travel destination and age because

  1. more visitors favour international travel.
  2. 35% of visitors under 55 years favour international travel.
  3. 45% of visitors 55 years and over favour domestic travel.
  4. 65% of visitors under 55 years favour domestic travel while 45% of visitors 55 years and over favour domestic travel.
  5. the percentage of visitors who prefer domestic travel is greater than the percentage of visitors who prefer international travel.

 
Part 3

The results could also be summarised in a two-way frequency table.

Which one of the following frequency tables could match the pecentaged segmented bar chart?

 

Show Answers Only

`text(Part 1:)\ A`

`text(Part 2:)\ D `

`text(Part 3:)\ A`

Show Worked Solution

`text(Part 1)`

`text{Preferred travel destination → categorical (nominal) variable}`

`text{Age → categorical (ordinal) variable}`

`=> A`
 

`text(Part 2)`

`text(Only option)\ D\ text(highlights a change in preference for domestic travel)`

`text(between the two age categories.)`

`=>D` 

 
`text(Part 3)`

♦ Mean mark 50%.

`text(Converting the frequency table data into percentages,)`

`text(consider option)\ A:`

`91/140 xx 100 = 65text(%),\ \ 49/140 xx 100 = 35text(%)`

`90/200 xx 100 = 45text(%), \ \ 110/200 xx 100 = 55text(%)`

`=> A`

CORE, FUR1 2020 VCAA 6 MC

A percentaged segmented bar chart would be an appropriate graphical tool to display the association between month of the year (January, February, March, etc.) and the

  1. monthly average rainfall (in millimetres).
  2. monthly mean temperature (in degrees Celsius).
  3. annual median wind speed (in kilometres per hour).
  4. monthly average rainfall (below average, average, above average).
  5. annual average temperature (in degrees Celsius).
Show Answers Only

`D`

Show Worked Solution

`text(The segments could be used to show below average,)`

`text(average and above average.)`

`=>  D`

CORE, FUR1 2018 VCAA 6 MC

Data was collected to investigate the association between the following two variables:

    • age (29 and under, 30–59, 60 and over)
    • uses public transport (yes, no)

Which one of the following is appropriate to use in the statistical analysis of this association?

  1. a scatterplot
  2. parallel box plots
  3. a least squares line
  4. a segmented bar chart
  5. the correlation coefficient r
Show Answers Only

`=> D`

Show Worked Solution

`text(A segmented bar chart is the best way to display the association)`

`text(between these two categorical variables.)`

`=> D`

CORE, FUR1 2017 VCAA 5-7 MC

A study was conducted to investigate the association between the number of moths caught in a moth trap (less than 250, 250–500, more than 500) and the trap type (sugar, scent, light). The results are summarised in the percentaged segmented bar chart below.
 

Part 1

There were 300 sugar traps.

The number of sugar traps that caught less than 250 moths is closest to

  1. 30
  2. 90
  3. 250
  4. 300
  5. 500

 
Part 2

The data displayed in the percentaged segmented bar chart supports the contention that there is an association between the number of moths caught in a moth trap and the trap type because

  1. most of the light traps contained less than 250 moths.
  2. 15% of the scent traps contained 500 or more moths.
  3. the percentage of sugar traps containing more than 500 moths is greater than the percentage of scent traps containing less than 500 moths.
  4. 20% of sugar traps contained more than 500 moths while 50% of light traps contained less than 250 moths.
  5. 20% of sugar traps contained more than 500 moths while 10% of light traps contained more than 500 moths.

 
Part 3

The variables number of moths (less than 250, 250–500, more than 500) and trap type (sugar, scent, light) are

  1. both nominal variables.
  2. both ordinal variables.
  3. a numerical variable and a categorical variable respectively.
  4. a nominal variable and an ordinal variable respectively.
  5. an ordinal variable and a nominal variable respectively.
Show Answers Only

`text(Part 1:)\ B`

`text(Part 2:)\ E`

`text(Part 3:)\ E`

Show Worked Solution

`text(Part 1)`

`text(Sugar traps that caught < 250)`

`= 30text(%) xx 300`

`= 90`

`=> B`

 

`text(Part 2)`

`text(An association should compare different)`

`text(trap types against the same value of)`

`text(number of moths caught.)`

`=> E`

 

`text(Part 3)`

`text{Number of moths (grouped) – ordinal variable}`

`text(Trap type – nominal variable)`

`=> E`

CORE, FUR2 2008 VCAA 2

In a larger survey, Years 6, 8 and 10 girls were asked what they did (walked, sat, stood, ran) for most of the time during a typical school lunch time. The results are displayed in the percentage segmented bar chart below.
 

CORE, FUR2 2008 VCAA 2 

Does the percentage segmented bar chart support the opinion that, for these girls, the lunch time activity (walked, sat or stood, ran) undertaken is associated with year level? Justify your answer by quoting appropriate percentages.   (2 marks)

Show Answers Only

`text(Yes. The table above shows that from year 6 to)`

`text(to year 8 to year 10, the percentage that ran)`

`text(changed from 78% to 40% to 10%.)`

Show Worked Solution

CORE, FUR2 2008 VCAA 2 Answer

`text(Yes. The table above shows that from year 6)`

MARKER’S COMMENT: An association does not have to be a consistent increase or decrease over the years.

`text(to year 8 to year 10, the percentage that ran)`

`text(changed from 78% to 40% to 10%.)`
 

CORE, FUR2 2014 VCAA 1

The segmented bar chart below shows the age distribution of people in three countries, Australia, India and Japan, for the year 2010.
 

Core, FUR2 2015 VCAA 1

  1. Write down the percentage of people in Australia who were aged 0 – 14 years in 2010.
  2. Write your answer, correct to the nearest percentage.  (1 mark)

  3. In 2010, the population of Japan was 128 000 000.
  4. How many people in Japan were aged 65 years and over in 2010?  (1 mark)

  5. From the graph above, it appears that there is no association between the percentage of people in the 15 – 64 age group and the country in which they live.
  6. Explain why, quoting appropriate percentages to support your explanation.  (1 mark)

Show Answers Only

  1. `text(19%)`
  2. `29\ 440\ 000`
  3. `text(The percentages of people in the 15 – 64 age group)` 
    `text(in each country is: Australia 67%, India 64%, and)` 
    `text(Japan 64%.)` 
    `text(S)text(ince the percentages are very close no matter which)`
    `text(country this age group belonged to, there is no association.)`

Show Worked Solution

a.   `text(19%)`

 

b.   `text(From the graph, 23% of Japan’s population is 65 or over.)`

`:.\ text(The number of people 65 or over)`

`=128\ 000\ 000 xx 23/100`

`= 29\ 440\ 000`

 

c.   `text(The percentages of people in the 15 – 64 age group)`

♦ Mean mark 41%.

`text(in each country is: Australia 67%, India 64%, and)`

`text(Japan 64%.)`

`text(S)text(ince the percentages are very close no matter which)`

`text(country this age group belonged to, there is no association.)`

CORE, FUR1 2007 VCAA 10 MC

The relationship between the variables

size of car (1 = small, 2 = medium, 3 = large)

and

salary level (1 = low, 2 = medium, 3 = high)

is best displayed using 

A.   a scatterplot.

B.   a histogram.

C.   parallel boxplots.

D.   a back-to-back stemplot.

E.   a percentaged segmented bar chart.

Show Answers Only

`E`

Show Worked Solution

`text(A segmented bar chart is required to effectively)`

♦ Mean mark 37%.

`text(display this information given the three)`

`text(sub-categories of each variable.)`

`rArr E`

CORE, FUR1 2010 VCAA 4 MC

The passengers on a train were asked why they travelled by train. Each reason, along with the percentage of passengers who gave that reason, is displayed in the segmented bar chart below.
 

CORE, FUR1 2010 VCAA 4 MC
 

The percentage of passengers who gave the reason ‘no car’ is closest to

A.   `text(14%)`

B.   `text(18%)`

C.   `text(26%)`

D.   `text(74%)`

E.   `text(88%)`

Show Answers Only

`A`

Show Worked Solution

`text(Percentage that stated “no car”)`

`=\ text(88% – 74%)`

`=\ text(14%)`

`=>  A`

CORE, FUR1 2009 VCAA 8 MC

An animal study was conducted to investigate the relationship between exposure to danger during sleep (high, medium, low) and chance of attack (above average, average, below average). The results are summarised in the percentage segmented bar chart below.
 


 

The percentage of animals whose exposure to danger during sleep is high, and whose chance of attack is below average, is closest to

A.     `4text(%)`

B.   `12text(%)`

C.   `28text(%)`

D.   `72text(%)`

E.   `86text(%)`

Show Answers Only

`E`

Show Worked Solution

`text(The correct percentage is the black bar section)`

`text(above the “high” column heading.)`

`=>E`