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Interpreting Data, SM-Bank 002

This graph shows a company's profits over a 4 year period.
 

  1. What were the company's total profits during this period?  (1 mark)
  2. What was the average yearly profit?  (1 mark)
  3. What percentage of total profit was made in the first year? Give your answer to 1 decimal place.  (2 mark)
  4. Explain how this graph could be misleading.  (2 marks)
Show Answers Only

a.    \($135\ 000\)

b.    \($33\ 750\)

c.    \(22.2\%\)

d.    \(\text{See worked solution}\)

Show Worked Solution
a.    \(\text{Total Profit}\) \(=30\ 000+2\times 40\ 000+25\ 000\)
    \(=$135\ 000\)

 

b.    \(\text{Average Profit}\) \(=\dfrac{$135\ 000}{4}\)
    \(=$33\ 750\)

 

c.    \(\text{Percentage Profit}\) \(=\dfrac{30\ 000}{135\ 000}\times 100\%\)
    \(=22.222\dots\%\)
    \(\approx 22.2\%\ \text{(1 d.p.)}\)

 
d.    \(\text{The vertical axis does not start at zero and could}\)

\(\text{give the impression that the years 2 and 3 profits are}\)

\(\text{twice as large as year 1, and 4 times as large as year 4.}\)

Interpreting Data, SM-Bank 001

Luke picked bananas during his university holidays last summer. He counted the total number of bananas he picked everyday and created the graph shown below.
 

 

  1. For how many days in total did Luke pick bananas?  (1 mark)
  2. On how many days did he pick less than 145 bananas?  (1 mark)
  3. Explain how this graph could be misleading.  (2 marks)
Show Answers Only

a.    \(30\ \text{days}\)

b.    \(17\ \text{days}\)

c.    \(\text{See worked solution}\)

Show Worked Solution
a.    \(\text{Days}\) \(=4+5+6+7+8\)
    \(=30\ \text{days}\)

 

b.    \(\text{Less than 145 bananas}\) \(=4+5+8\)
    \(=17\ \text{days}\)

 

c.    \(\text{The vertical axis starts at 135 and could give}\)

\(\text{the impress that the number of bananas picked}\)

\(\text{on 6 of the days was more than twice the number}\)

\(\text{picked on 4.}\)

\(\text{The actual difference being only}\)

\(= 152-139=15\ \text{bananas}\)

Statistics, STD2 S1 2006 HSC 24a

2UG-2006-24a

List TWO ways in which this graph is misleading.  (2 marks)

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`text(Reasons the graph is misleading include)`

`text(- the columns are a different widths/volumes)`

`text(- the vertical axis doesn’t start at zero)`

Show Worked Solution

`text(Reasons the graph is misleading include)`

`text(- the columns are a different widths/volumes)`

`text(- the vertical axis doesn’t start at zero)`

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)

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)

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.)`