The mean, median and mode are all types of average, but each one summarises data differently. Choosing the right average depends on the type of data and whether there are extreme values (outliers) that could distort the result. Knowing which to use — and why — is a key KS3 exam skill.
What does each average actually measure?
Each average answers the same basic question ("what is a typical value?") in a different way:
| Average | How it is calculated | Best used when |
|---|---|---|
| Mean | Sum of all values ÷ number of values | Data is numerical and has no extreme outliers |
| Median | Middle value of ordered data | Data has outliers or is skewed; income data |
| Mode | Most frequent value | Data is categorical (e.g. shoe sizes, colours) or you need the most popular item |
All three are valid averages; none is universally "the best". The skill is matching the right average to the situation.
When should you use the mean?
Use the mean when:
- Data is numerical (not categories).
- There are no extreme outliers — unusual values that would drag the mean far from a typical data point.
- All values carry equal importance and you want to use every data point.
Example: Test scores for a class of 10 students: 55, 58, 60, 62, 65, 67, 70, 72, 75, 76.
Mean = (55 + 58 + 60 + 62 + 65 + 67 + 70 + 72 + 75 + 76) ÷ 10 = 660 ÷ 10 = 66
The data is roughly symmetric (no extreme values), so the mean of 66 gives a fair picture of a typical score.
When should you use the median?
Use the median when:
- Data contains outliers that would distort the mean.
- Data is skewed (bunched at one end with a long tail at the other).
- You want to find the middle of a ranked list rather than a calculated average.
Example: Salaries of five staff at a small company: £18 000, £22 000, £24 000, £26 000, £150 000.
Mean = (18 000 + 22 000 + 24 000 + 26 000 + 150 000) ÷ 5 = 240 000 ÷ 5 = £48 000
Median = middle value when ordered = £24 000
The £150 000 salary (the director's) is an extreme outlier. The mean of £48 000 is higher than four out of five actual salaries — it gives a misleading picture of a "typical" salary. The median of £24 000 is far more representative of what most staff earn.
When should you use the mode?
Use the mode when:
- Data is categorical (non-numerical), such as colours, shoe sizes or makes of car.
- You need the most popular or most common item — for example, which product sells most.
- There is a clear single most-frequent value.
Example: A shoe shop sells the following sizes in one day: 5, 5, 6, 6, 6, 7, 7, 8, 9, 9.
Mode = 6 (appears 3 times, more than any other size)
The mean shoe size (6.8) and median (6.5) are both non-integer values — no one buys a size 6.5 or 6.8 shoe. The mode gives the most useful information for ordering stock.
How do outliers affect each average?
| Average | Effect of an outlier |
|---|---|
| Mean | Strongly affected — pulled towards the outlier |
| Median | Not affected — the middle value stays the same |
| Mode | Not affected — frequency is unchanged by adding an extreme value |
Worked example: Data set: 3, 5, 6, 7, 8. Add an outlier: 3, 5, 6, 7, 8, 50.
- Old mean = 29/5 = 5.8; new mean = 79/6 = 13.2 (more than doubled)
- Old median = 6; new median = (6+7)/2 = 6.5 (barely changed)
- Mode: no change — still no repeated value
This shows clearly why the median is preferred when outliers are present.
How do you answer "which average is most appropriate?" in an exam?
Exam questions often ask you to state which average a given calculation used and whether it is "most appropriate". Use this checklist:
- Is there an outlier? If yes, the mean is misleading → prefer median.
- Is the data categorical? If yes → mode.
- Is the data numerical and symmetric, with no outliers? → mean is fine.
- Does the question say "most popular"? → mode.
- Does the question say "typical" or "representative"? → depends on whether outliers are present (median if yes, mean if no).
Always justify your choice with one sentence, for example: "The median is most appropriate because the outlier of £150 000 distorts the mean."
Frequently asked questions
Can a data set have more than one mode?
Yes. If two or more values share the highest frequency, there are multiple modes — the data is bimodal (two modes) or multimodal (more than two). If every value appears exactly once, there is no mode. This is an important distinction when choosing the mode as your average.
Is the mean always between the smallest and largest values?
Yes, always. The mean of any data set is at least as large as the minimum value and at most as large as the maximum value. This gives you a quick check: if your calculated mean falls outside the range of the data, you have made an arithmetic error.
Why do newspapers often use the mean but analysts prefer the median for income data?
Because income data in the UK is heavily right-skewed — most people earn moderate incomes, but a small number of very high earners drag the mean significantly above what most people earn. The Office for National Statistics publishes median household income precisely because the mean would give a misleading picture of typical earnings.
How do I decide between median and mean when the data looks roughly symmetrical?
When data is roughly symmetrical and has no obvious outliers, the mean and median are close in value. Either is acceptable, but the mean is often preferred because it uses every data point and is easier to use in further calculations. Only switch to the median when there is a clear reason — an outlier, strong skew or categorical data.
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