Choosing the Right Average
Master Choosing the Right Average for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. The best average depends on the data: the mode for categories, the median for skewed data, and the mean for symmetric data.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
Topic overview
Choosing the right average means matching the average to the data and the purpose, and justifying the choice.
The mean uses every value, so it is best for symmetrical data with no outliers. Its weakness is that a single extreme value distorts it. The median depends only on position, so it is unaffected by outliers and is the right choice for skewed data such as salaries or house prices.
The mode is the only average available for qualitative data, and it is useful when the most common value is what matters — a shoe shop cares about the most popular size, not the mean size. Questions almost always ask for a reason, so naming the average alone will not earn full marks.
Revision notes
When to use each
Mean: symmetrical data with no outliers, where every value should count.
Median: skewed data or data containing outliers, since it is unaffected by extremes. Mode: qualitative data, or when the most common value is what matters.
Strengths and weaknesses
Mean: uses all the data, but is distorted by outliers.
Median: unaffected by outliers, but ignores the actual values of most of the data. Mode: works with any data type, but may not exist or may not be unique.
Justifying the choice
Questions ask for a reason, not just a name.
Say what the data looks like and why that average suits it — for example, salaries include a few very high earners, so the median is better because the mean would be pulled upwards.
Key points
- The mean uses every value.
- The mean is distorted by outliers.
- The median is unaffected by extreme values.
- The median suits skewed data.
- The mode is the only average for qualitative data.
- Always justify the choice of average.
Worked examples
Example 1
A data set of salaries includes one very high value. State which average is most appropriate and why. [2 marks]
Working
Example 2
A shop records the shoe sizes it sells. State which average is most useful and why. [2 marks]
Working
Example 3
Give one disadvantage of using the median. [1 mark]
Working
Common mistakes
Naming an average without justifying it.
The reason usually carries a mark of its own.
Using the mean for skewed data.
Outliers distort it, so the median is normally better.
Saying the mode is always available.
There may be no mode, or more than one.
Giving a vague reason such as 'it is more accurate'.
Say specifically what the data is like and why the average suits it.
Exam tips
- Always give a reason alongside the average you choose.
- Look for outliers before deciding.
- Use the mode when the most common value is what matters.
- Learn one strength and one weakness of each.
Key terms
- Skewed data
- Data with a long tail in one direction.
- Outlier
- An extreme value distorting the mean.
- Representative
- Reflecting a typical value of the data.
- Qualitative data
- Descriptive data for which only the mode is available.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.