๐ฏ Learning Objectives
- interpret statistical summaries in context;
- recognise misleading axes and graphs;
- identify sampling and response bias;
- distinguish association from causation;
- evaluate whether evidence supports a claim.
Introduction
This lesson develops Interpreting and Critiquing Data from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Misleading Graphs
A vertical axis beginning at 95 instead of 0 may make a small change from 98 to 100 look dramatic.
A graph can be mathematically accurate yet visually misleading.
โ ๏ธ Spot the Misleading Graph
The same values can appear dramatically different when the vertical axis is truncated.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- A cafรฉ asks only morning customers about preferred opening hours. Identify a possible bias.
- A graph begins at 99 and ends at 102. Why might it mislead?
- Two variables rise together. What can you safely conclude?
- Why should the chosen average be stated?
- Give one sign that a claim may be unreliable.
โ Check Your Work
Show answers and working
- Morning customers may not represent afternoon or evening customers.
- The narrow scale visually exaggerates a small difference.
- Only that they are associated in this data; causation has not been established.
- Mean, median and mode can give different impressions, especially with outliers or skew.
- For example: a tiny or biased sample, vague question, missing source, truncated axis or unsupported causal claim.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Critical thinking is part of statistics.
- Always examine source, sample, scale, measure and claim.