NSW Mathematics Standard 11 - 2020 Edition
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10.09 Comparing data representations
Lesson

So far we have covered a range of different chart types for representing data. In this final topic, we consider various other charts, including pictograms, sector graphs (pie charts), line graphs, and divided bar charts.

 

Which type of chart to use?

The type of chart we choose will depend primarily on the type and size of the data.

  • Type: some charts are more suitable for numerical data, while others are better at representing categorical data.
Numerical Categorical
dot plot pictogram
stem-and-leaf plot divided bar chart
line graph sector graph (pie chart)
frequency polygon bar chart
histogram Pareto chart
box plot  
  • Size: some display types (like sector graphs, pictograms, divided bar charts and dot plots) are not suitable for large data sets.

 

Practice questions

Question 1

The grouped bar chart shows customer satisfaction ratings for different cars, broken down by gender. The red rows represent males; the blue rows, females.

Which of the following statements are true?

  1. Honda received the highest ratings.

    True

    A

    False

    B

    True

    A

    False

    B
  2. Ford received the lowest ratings among Males.

    True

    A

    False

    B

    True

    A

    False

    B
  3. Both genders agree on the rank order in which the cars are rated.

    True

    A

    False

    B

    True

    A

    False

    B
  4. As a group, the women seem to be tougher raters; they gave lower ratings to each car than the men gave.

    True

    A

    False

    B

    True

    A

    False

    B
  5. Females prefered the cars that were red.

    True

    A

    False

    B

    True

    A

    False

    B

Question 2

The graph represents the number of iTunes sales (in millions) and iPod sales (in hundreds of thousands) every 3 months between 2003 and 2007.

  1. How many iTunes sales were there in the first quarter of 2006 (2006 Q1)?

  2. How many iPod sales were there in the first quarter of 2006?

  3. How many more iTunes sales were there than iPod sales in the first quarter of 2007?

  4. How many iTunes sales were there in 2006?

 

Misleading graphs

Charts are often used in the media to show comparisons and describe trends. At times, they are also used to misrepresent information and promote a biased view.

Some of the ways in which a chart can be misleading include:

  • Biased labelling
  • Missing a scale on one of the axes
  • Not starting the vertical axis scale at zero
  • Using a scale that isn't uniform
  • Having an inappropriate scale for the given data (making variations seem less important than they are)
  • Only displaying a select portion of the data
  • Using the wrong type of chart
  • Using inappropriate scaling on chart elements like bars or sectors. 
  • Using unconventional methods

 

 

Practice question

Question 3

The Australian Labour Party released this graph after Tony Abbot was elected as Prime Minister.

  1. Which of the following comments apply:

    This graph is misleading because the scale on the vertical axis is not uniform.

    A

    This graph is misleading because it assumes that there are always an equal number of male and female cabinet members to choose from

    B

    This graph is misleading because it assumes all cabinet sizes are the same.

    C

    This graph is misleading because there are no European countries included

    D

    This graph is misleading because the scale on the vertical axis is not uniform.

    A

    This graph is misleading because it assumes that there are always an equal number of male and female cabinet members to choose from

    B

    This graph is misleading because it assumes all cabinet sizes are the same.

    C

    This graph is misleading because there are no European countries included

    D

Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-7

develops and carries out simple statistical processes to answer questions posed

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