Explain the meaning of the following terms in relation to misrepresenting data:
Cherry picking
Comparing apples and oranges
State the type of data manipulation described in each of the following examples:
There is a strong correlation between temperature and ice-cream consumption. Therefore rising temperatures cause higher ice-cream consumption.
75\% of a high school class surveyed said they like sport. Therefore all high school students like sport.
Asking an air traffic controller about his stress levels compared to a four year old child.
Lachlan asks 120 Year 12 students at his school how much time they spend on homework per night. 78 Year 12 students say they do more than 3 hours. At a meeting of the student council, Lachlan reports "65\% of students at this school do too much homework."
Determine whether the following statements explain why Lachlan's report is misleading:
The survey does not represent the population of the school.
The question should have been multiple choice.
The question was biased.
The sample size was too small.
A newspaper states: "Oil prices have risen by 33\% over the last two years." The article states that in 2018, the oil prices increased by 10\% and in 2019, the oil price increased by 23\%.
Determine whether the following statements are true or false:
The headline is true and accurate.
We need to know the prices to determine whether this statement is accurate.
An increase of 10\% followed by an increase of 23\% does not give an increase of 33\% overall.
A graph is required for more complete analysis.
An online company asks all its customers to complete a survey and 58\% respond. In the survey, there was a question which asked “How happy are you with our service?”. Respondents could tick either “Very Happy” or “Somewhat Happy”.
In their annual newsletter, the company wrote an article reporting “100\% of customers are happy with our service”.
Explain why this claim is misleading.
In the polls for an upcoming election, various polls are analysed to see who is likely to win the election. Most polls put Kodos ahead of Kang by between 10\% and 12\%. A few polls have Kang ahead of Kodos by a few percentage points.
Kang tells his followers that they are sure to win the election based on the latest polls.
Explain why this statement misrepresents the statistics.
In NSW, data collected on assaults occurring in hospitals showed that from 2006 to 2011, the number of assaults increased, from 2011 to 2014, the number of assaults remained constant and in 2015, there was a drop in the number of assaults.
Based on this, a newspaper reported “Assaults in hospitals have risen dramatically from 2006 to 2015”.
Explain why this statement misrepresents the statistics.
Determine whether the following statements, that describe how this graph might misrepresent the statistics, are true or false:
The wrong graph type was used.
The graph doesn't start at 0.
The scale on the vertical axis is not uniform.
Explain why a pie chart is inappropriate for the data shown below:
The pie chart shows the number of nuclear weapons possessed by each country:
Source: Time Magazine
Considering only the size of the slices (i.e. ignoring the numbers), which country has the largest nuclear stockpile?
Looking only at the numbers listed for each country, which country has the largest nuclear stockpile?
Has the pie chart been drawn accurately?
Consider the following graph:
Describe two features of this graph that might cause it to misrepresent the statistics:
Consider the following line graph:
Source: Brookings report on American education.
The bottom section of the graph has been cropped. Describe the effect this may have on interpreting the graph.
The labels on the horizontal axis are not evenly spaced. Explain why this may be misleading.
The Australian Labour Party released this graph after Tony Abbot was elected as Prime Minister:
Determine whether the following statements, that describe how this graph might misrepresent the statistics, are true or false:
The scale on the vertical axis is not uniform.
There are no European countries included.
It assumes that there are always an equal number of male and female cabinet members to choose from.
It assumes all cabinet sizes are the same.
Compare the following two graphs and explain which graph is misleading and why:
Explain why the following graph is misleading:
The following graph was shown on an Argentinian news service with the comment that 'Argentina's testing rate for Covid-19 is almost as high as that of the United States'.
Source: Reddit May 2020
Explain why the graph and comment are misleading.
Redraw the graph correctly.
Consider the given column graph:
Why is this a particularly poor example of a graph with broken axes?
Explain why it is not generally good practice to use a vertical scale with a broken axis for column graphs.
Describe a graphical display that would be better suited to this situation.
Consider the following line graph:
What feature is missing from the graph?
Explain why this might be misleading.
Consider the following line graphs of the same set of sales figures:
Describe how the difference in scale between the two graphs might be misleading.