By the end of this section you should: ● understand that statistics can be misused ● be able to identify misleading statistics
Statistics are very important to allow us to identify patterns and relationships and allow us to make predictions based on existing data. Sometimes, however statistics can be misused.
Here are some ways in which this can happen. ●
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Quoting statistics based on poor samples: If a sample is too small or non-representative the statistics developed from it will not be reliable.
Choice of the average value for a sample: Since the mean, mode and median are all averages, we can calculate all three and choose the one which is closest to the result we want, when a diff erent average value might be more appropriate/accurate.
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Using detached statistics: Statements like ‘one-third less’ indicate that something is better than something else, but it doesn’t mean much unless we know what it is in relation to.
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Formatting graphs to mislead the eye: The two bar charts opposite represent the exact same data.
The fi rst chart shows the scale starting from 0 whereas in the second the scale starts at 4. This emphasises the small diff erences in the heights of the bars. Changes to the scales of a graph can dramatically alter the look of the graph.
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4 5 6
1 3
2
Designing questions to be used on a survey that will bias the results: Survey questions can be designed to produce a more positive or negative response. These are called leading questions and should be avoided.
4.0 4.5 5.0 5.5
Worked example
Examine the data representation shown on the right and comment on whether you think it is misleading or not. Justify your answer.
40 42
38 36 34
35%
6 months ago
Solution Now
Unemployment rates soar
39.6%
Discuss and discover
(i) Using newspapers, magazines, or the internet, fi nd a graph or statistic that creates a false impression.
(ii) Describe how the graph or statistic creates a false impression. (iii) Why might the misleading graph or statistic be used? (iv) How could the graph or statistic be changed to present the data accurately?