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

Interpreting Data, SM-Bank 003

Margaret is preparing a report for her supervisor regarding costs for the recent staff development day.

Below is the graph Margaret prepared summarising the cost of the staff lunch for the day.

  1. What type of graph has been used to display the information?  (1 mark)
  2. Identify the two variables Margaret has used in this graph?  (1 mark)
  3. What is the cost of lunch per attendee?  (1 mark)
  4. If the total cost for the staff lunch was $85, how many attendees were there?  (1 mark)
  5. Briefly describe what happens to the total cost of the staff lunch as the number of attendees increases?  (1 mark)
Show Answers Only

a.    \(\text{Line graph}\)

b.    \(\text{Number of Attendees and Cost}\)

c.    \($5\)

d.    \(17\)

e.    \(\text{As the number of attendees increases the cost increases.}\)

Show Worked Solution

a.    \(\text{Line graph}\)

b.    \(\text{Number of Attendees and Cost}\)

c.    \(\text{From the graph, the cost per attendee}= $5\)

d.    \(\text{Number of Attendees}\)

\(=$85\ ÷\ 5\)

\(=17\)

e.    \(\text{As the number of attendees increases the cost increases.}\)

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 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 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

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

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

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

\(\Rightarrow B\)