Raw data on its own rarely tells a clear story. Averages are how scientists compress a whole set of measurements into a single number worth talking about — but choosing the wrong average can quietly mislead.
Seven quiz scores, sitting side by side, do not tell a story on their own — a reader would have to hold all seven numbers in their head at once. Statistics solves this by compressing a whole data set into a single representative number. The catch is that there are three different "representative numbers" to choose from, and picking the wrong one can quietly distort the picture.
The mean is what most people simply call "the average." It is calculated by adding up every value in a data set and dividing by how many values there are.
Five students score 70, 75, 80, 85, and 90 on a test. The mean is (70 + 75 + 80 + 85 + 90) ÷ 5 = 400 ÷ 5 = 80.
The mean uses every single value in the calculation, which is exactly what makes it powerful — and exactly what makes it vulnerable. A single unusually high or low value, called an outlier, can pull the mean noticeably away from where most of the data actually sits.
The median is the middle value once all the numbers are arranged in order from smallest to largest. If there is an even number of values, the median is the average of the two middle numbers.
For the values 3, 7, 9, 15, 21 (already in order), the median is the middle value: 9. For an even-sized set like 4, 8, 10, 14, the median is the average of the two middle values: (8 + 10) ÷ 2 = 9.
Because the median only cares about position, not exact size, it barely moves even when one value in the data set is extreme — making it far more resistant to outliers than the mean.
The mode is the value that appears most often in a data set. Unlike the mean and median, the mode can be used even with non-numeric data, such as favourite colours or types of pets.
In the data set 4, 6, 6, 6, 9, 12, the mode is 6, since it appears more often than any other value. A data set can also have more than one mode, or none at all if every value appears the same number of times.
The chart below shows seven quiz scores. Six students scored in a similar range, but one student — perhaps rushed or unwell that day — scored far lower. Watch what this does to the mean compared to the median.
| Average | Best Used When | Weakness |
|---|---|---|
| Mean | Data is fairly evenly spread, with no extreme values | Easily distorted by outliers |
| Median | Data contains outliers or is unevenly spread | Ignores the exact size of every value |
| Mode | Data is categorical, or you need the most common result | May not exist, or may not be near the "typical" value |
National income statistics are a classic case of this choice mattering. If a small number of people earn extremely high incomes, the mean income gets pulled well above what a typical person actually earns. The median income — the exact middle of the distribution — is far less distorted by those few very high earners, which is why economists and journalists usually report median income rather than mean income when describing what a "typical" household earns.
None of the three averages is universally "correct" — each answers a slightly different question. Part of thinking statistically is recognising which question is actually being asked, and choosing the average that answers it honestly rather than the one that looks the most impressive.
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