Identify bias & misleading data; pose questions
Theory
Data can give the wrong idea if a graph is drawn unfairly or a survey is not fair. A graph can mislead with a cut scale, uneven steps or missing labels; a survey can be biased if it asks the wrong people or asks a leading question. This Year 6 maths page shows how to spot these problems and how to pose fair survey questions.
A graph is misleading when it makes the data look different from what it really is. Column heights only compare fairly if the scale starts at \(0\) and goes up in equal steps.
A sample is the group of people asked. It is biased when it is not like the whole group, for example asking only people at a skate park about their favourite sport.
A sample that is too small may not represent everyone: \(6\) students cannot speak for a school of \(600\).
A leading question pushes people to one answer ("Don’t you agree that ...?"). A good question is short, neutral, asks one thing, and has answer choices that do not overlap.
Checklist for a fair graph and a fair survey:
| Check | What to look for |
|---|---|
| Scale | starts at 0, equal steps |
| Labels | title, axis labels, units |
| Pictures | all symbols the same size |
| Sample | big enough, like the whole group |
| Question | neutral, one thing at a time |
| Answer choices | cover everyone, no overlaps |
How to check a graph
- Look for a title and labels on both axes.
- Check the scale starts at \(0\) and the steps are equal.
- Read the actual numbers before trusting how tall the columns look.
How to write a good survey question
- Ask about one thing only.
- Use neutral words (no "great", "terrible", "don’t you agree").
- Give answer choices that do not overlap and include "other".
- Ask a big enough sample from every part of the group.
| \(59 - 52\) | \(=\) | \(7\) |
No. Sales went from \(52\) to \(59\), a rise of only \(7\). The scale starts at \(50\), which cuts off the bottom of every column.
| \(9 \div 2\) | \(=\) | \(4.5\) |
Thursday looks \(4.5\) times as tall. That is not fair: \(59\) is only \(7\) more than \(52\).
The steps are \(25\), \(25\), \(50\), \(100\): the same space stands for different amounts, so big values look smaller than they are.
Students at a skate park are more likely to choose skateboarding, so the sample is biased.
| \(600 \div 6\) | \(=\) | \(100\) |
He asked only \(1\) in every \(100\) students, and only his friends, so the sample is too small and not chosen fairly.
"Should the library get more beanbags? Yes / No / Not sure."
Someone who sleeps \(9\) hours could tick two boxes. Fix: "less than \(9\)", "\(9\) up to \(10\)", "\(10\) or more".
There is no “other” box, so someone whose favourite is mango cannot answer. Add an “other” choice.
The second picture covers \(4\) times the space, so \(80\) looks like \(4\) times \(40\) instead of \(2\) times.
Common pitfalls
Frequently asked questions
Why should a column graph start at zero?
So the column heights are in proportion to the numbers they show.
What is a biased sample?
A group of people asked that is not like the whole group, so the results lean one way.
What is a leading question?
A question worded to push people towards one answer.
How big should a sample be?
Big enough to represent the group: more people from every part of the group give a fairer result.
What makes a good survey question?
It is short, neutral, asks one thing, and has answer choices that cover everyone without overlapping.