Identify bias & misleading data; pose questions
Theory
Data can mislead when a graph is drawn unfairly or a sample is chosen badly. Check that the scale starts at \(0\), the graph is labelled, and the sample is large and represents everyone.
Data misleads when a graph is drawn unfairly or a sample is chosen badly, even though the numbers are correct.
A fair column graph starts its scale at \(0\), rises in equal steps, has a title and labels both axes.
Cutting the scale so it starts above \(0\) makes small differences look far bigger than they are.
A survey is fair only when its sample is big enough and represents everyone, and the question does not lead the answer.
Check three things before trusting a graph or a survey.
| Check | Fair | Unfair |
|---|---|---|
| Scale | starts at \(0\) | cut off above \(0\) |
| Labels | title and axes | missing |
| Sample | large, mixed | tiny or one-sided |
How to judge whether data misleads
- Look at where the vertical scale starts — a cut-off axis exaggerates differences.
- Check for a title and axis labels.
- Judge the sample: is it big enough and does it represent everyone?
- Read the survey question — does it lead the answer?
Subtract the two values.
| \(88-82\) | \(=\) | \(6\) |
Small, even though the cut graph looks huge.
A reader cannot tell what it is about or what the numbers count, so it cannot be trusted.
Far too few, and all play netball.
| \(400-8\) | \(=\) | \(392\) not asked |
The sample is biased.
It pushes the answer towards apples, so the results are not fair. Offer clear, equal choices instead.
Common pitfalls
Frequently asked questions
How can a graph mislead if the numbers are right?
By how it is drawn. Cutting the scale so it starts above \(0\) makes small differences look huge, even though the values have not changed.
Why should the scale start at zero?
So heights compare fairly. When the scale is cut off, only the tops of the columns are drawn, so a small gap looks like a big one.
What makes a survey sample biased?
Asking too few people, or only one kind of person. If you ask only netball players about sport, netball is almost certain to win.
What is a leading question?
One that pushes the answer one way, like “Don't you agree apples are best?”. It makes the results unfair, so offer clear, equal choices instead.
How do I pose a fair survey question?
Make it clear, offer choices that do not overlap, and do not hint at an answer. Sampling a large, mixed group keeps the results fair.