The mean (often called the arithmetic average) is the sum of all values divided by how many values there are. The median is the middle value after the data are sorted—or, with an even number of values, the average of the two middle values. The mean uses every value and can be pulled by extremes; the median marks the midpoint in rank. Which is more useful depends on what “typical” means for the question.
How are the mean and median calculated?
Mean: add and divide
Add every observation, then divide the total by the number of observations. For example, for 2, 4, and 9, the mean is (2 + 4 + 9) ÷ 3 = 5.
Median: sort and find the middle
Put the values in order from smallest to largest. If there is an odd number of values, the median is the one in the middle. If there is an even number, take the arithmetic average of the two middle values. The Australian Bureau of Statistics explains both calculations in its guide to measures of central tendency.
For example, in 1, 4, 7, 10, the median is (4 + 7) ÷ 2 = 5.5. The mean is 5.5 too, but that agreement is coincidental: the two statistics are calculated differently.
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Why can the mean and median differ?
Every value contributes to the mean, so an unusually large or small value can move it. The median depends on the middle rank, so a change to an extreme value often leaves it unchanged. This makes the median comparatively resistant to outliers, but it does not make the mean incorrect: the mean still describes the arithmetic balance point.
Skew can make the difference especially visible. In a right-skewed distribution, a long high-value tail tends to pull the mean upward; in a left-skewed distribution, a long low-value tail tends to pull it downward. The median can better express the midpoint-ranked observation when that is what “typical” is meant to describe. For more on how distribution shape affects measures of location, see the National Institute of Standards and Technology’s explanation.
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An official teaching example
The Australian Bureau of Statistics gives retirement ages of 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, and 60. The median is 57 years; the total is 623 across 11 observations, so the mean is 56.6 years. These are values from an 11-person teaching example published in 2023, not a population estimate. In an even-count example, the ABS uses middle values of 56 and 57, making the median 56.5 years—also a worked-example value.
Which should you use?
| Question or situation | Useful measure | Why |
|---|---|---|
| You want the arithmetic balance point, and the magnitude of every observation matters. | Mean | Every value contributes to the sum. |
| You want the middle-ranked value, especially when the data are skewed or contain extreme values. | Median | It is less affected by extremes than the mean. |
| The data are skewed, but “typical” is unclear. | Consider reporting both, with a description of the distribution. | Mean and median describe different aspects of the center; the right choice depends on the purpose. |
| You want to describe the middle worker’s earnings in a positively skewed earnings distribution. | Median | A small number of very high earnings can raise the mean above the median, as the ABS explains in its average earnings guide. |
For a symmetric distribution, mean, median, and mode can coincide, according to the ABS. That does not make the mean and median interchangeable; it only means their values happen to match in that case.
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What does “average” mean in a money conversation?
“Average” often means the mean, but a person may use the word without specifying a calculation. In a skewed context such as earnings, state whether you mean the mean or median. The mean answers a balance-point question; the median answers a middle-ranked-value question. Naming the statistic helps readers understand what the number says—and what it does not.
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