Many IB Mathematics: Applications & Interpretation students automatically calculate the mean and assume it gives the best summary of a dataset. When examiners then expect discussion of the median instead, this can feel confusing or unfair — especially if the mean was calculated correctly.
IB emphasises the median because “average” does not always mean “mean.” In many real-world datasets, the median gives a more realistic picture of a typical value. Understanding when and why this happens is a key interpretation skill in AI Maths.
What the Median Actually Represents
The median is the middle value when data is ordered.
Unlike the mean, it does not depend on the size of extreme values. IB expects students to recognise that the median reflects what is typical, rather than what is mathematically balanced.
This makes the median especially useful in skewed distributions.
Why the Median Is Less Affected by Outliers
Outliers can pull the mean up or down significantly.
The median, however, only depends on position, not magnitude. Whether an extreme value is slightly unusual or extremely large, it does not change the median unless it crosses the middle position. IB uses this contrast to test whether students understand robustness in statistics.
When the Median Gives a More Realistic Picture
The median is often more appropriate when:
- Data is skewed
- There are extreme values
- The context involves inequality or spread
- Typical experience matters more than totals
Examples include income, house prices, waiting times, or test scores. IB expects students to justify why the median may better represent “most people” in such contexts.
Why Students Default to the Mean
The mean is often taught as the standard average.
IB challenges this habit deliberately. Students who default to the mean without checking distribution or context often lose interpretation marks. The key is not choosing the median automatically, but choosing thoughtfully.
Why This Matters in Applications & Interpretation
AI Maths focuses on real-world decision-making.
IB wants students to think critically about which summary statistic best represents the situation. Choosing the median when appropriate shows deeper understanding than calculating the mean mechanically.
How IB Expects You to Compare Mean and Median
IB expects students to:
- Identify skewness or outliers
- Comment on how these affect the mean
- Explain why the median may be more representative
- Link reasoning to context
Even one clear sentence comparing the two can earn multiple marks.
Common Student Mistakes
Students frequently:
- Assume the mean is always best
- Calculate both values but explain neither
- Ignore skewness
- Fail to link statistics to context
- State results without justification
Most lost marks come from missing interpretation.
Exam Tips for Mean vs Median Questions
Always look at the distribution first. Check for skewness or outliers. Ask what “typical” means in context. If the median is more representative, say why. IB rewards explanation over calculation.
Frequently Asked Questions
Is the median always better than the mean?
No. For symmetric data without outliers, the mean works well. IB expects judgement, not rules.
Should I always calculate both?
Only if asked. What matters more is explaining which one is appropriate.
Can I lose marks for using the mean when the median is better?
Yes, especially if interpretation marks are available. IB wants thoughtful choice.
RevisionDojo Call to Action
The median is powerful because it resists distortion. RevisionDojo helps IB Applications & Interpretation students learn when to use the mean, when the median is better, and how to explain this clearly in exams. If statistics questions feel harsh despite correct maths, RevisionDojo is the best place to build strong interpretation skills.
