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Displaying Data, SM-Bank 039 MC

Joseph asked children in his class what their favourite sport was.

Their answers were used to draw the sector graph below.
 

   

Around a quarter of the students preferred which sport?

  1. Netball
  2. Soccer
  3. Cricket
  4. Basketball
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Soccer represents one quarter of the graph.}\)

\(\Rightarrow B\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

    --- 2 WORK AREA LINES (style=lined) ---

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

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

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

    --- 1 WORK AREA LINES (style=lined) ---

  2. What fraction of the animals were rhinos?  (1 mark)

    --- 1 WORK AREA LINES (style=lined) ---

  3. How many big game animals were in the park in total?  (2 marks)

    --- 3 WORK AREA LINES (style=lined) ---

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

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

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

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

`7`

Show Worked Solution

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

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

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

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

\(=7\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

    --- 3 WORK AREA LINES (style=lined) ---

  2. How much money did Kat spend on meals?  (2 marks)

    --- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

a.    \($396\)

b.    \($264\)

Show Worked Solution

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

\(=33\%\times 1200\)

\(=$396\)

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

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

\(=$264\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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

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

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

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

\(\Rightarrow B\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

Displaying Data, SM-Bank 022 MC

This diagram shows the proportion of milkshake flavours sold by a corner store over a 1 month period.
 

 
Which flavour makes up 55% of the milkshakes sold?

  1. vanilla
  2. strawberry
  3. caramel
  4. chocolate
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Chocolate takes up slightly more than half the sector graph.}\)

\(\Rightarrow D\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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

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

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

\(\Rightarrow B\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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

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

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

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

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

\(\Rightarrow B\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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

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

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

\(\Rightarrow C\)

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

\(5\)

Show Worked Solution

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

\(= 35-15\)

\(= 20\)

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

\(= 45-20\)

\(= 25\)
 

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

Filed Under: Displaying Data Tagged With: num-title-ct-core, smc-5076-15-Sector graphs and Divided Bar graphs

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)

    --- 1 WORK AREA LINES (style=lined) ---

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)

    --- 4 WORK AREA LINES (style=lined) ---

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.)`

Filed Under: Bar Charts and Histograms, Bar Charts and Histograms (Std 2), Bar Charts and Histograms (Std2-2027), Bar Charts and Histograms (Y12), Bar Charts, Histograms and Other Graphs (Std 1), Displaying Data, Other Chart Types (Y12), Other Charts (Std 2), Other Charts (Std2-2027), Other Graphs Tagged With: Band 4, common-content, num-title-ct-core, num-title-qs-hsc, smc-1128-10-Bar Charts, smc-5076-15-Sector graphs and Divided Bar graphs, smc-5077-10-Misleading graphs, smc-6310-10-Bar Charts, smc-6311-30-Other Charts, smc-821-10-Bar Charts, smc-822-40-Other Charts, smc-997-10-Bar Charts, smc-998-40-Other Charts

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`

Filed Under: Bar Charts, Histograms and Other Graphs (Std 1), Displaying Data, Other Chart Types (Y12), Other Charts (Std 2), Other Charts (Std2-2027), Other Graphs Tagged With: Band 3, common-content, num-title-ct-core, num-title-qs-hsc, smc-1128-28-Other Charts, smc-5076-15-Sector graphs and Divided Bar graphs, smc-6311-30-Other Charts, smc-822-40-Other Charts, smc-998-40-Other Charts

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.)`

Filed Under: Bar Charts, Histograms and Other Graphs (Std 1), Displaying Data, Other Chart Types (Y12), Other Charts (Std 2), Other Graphs Tagged With: Band 4, common-content, num-title-ct-core, num-title-qs-hsc, smc-1128-28-Other Charts, smc-5076-15-Sector graphs and Divided Bar graphs, smc-822-40-Other Charts, smc-998-40-Other Charts

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