Direct comparison
Average vs Median: What Is the Difference?
Average versus median explained: how the mean and median are calculated, why extreme values pull the mean, and which to report, with NIST and Census sources.
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How do Average (mean), Median compare side by side?
The table below compares Average (mean), Median across 12 procurement-relevant dimensions, from definition through source.
Side-by-side comparison
| Dimension | Average (mean) | Median |
|---|---|---|
| Definition | The mean: the sum of the data points divided by the number of data points. NIST notes it is the value most commonly called the average. | The median: the value with half the data smaller and half the data larger. |
| How it is calculated | Add every value, then divide by how many values there are. | Sort the values from smallest to largest, then take the middle one. |
| Odd and even numbers of values | Same rule either way. | Odd N: the middle value, Y(N+1)/2. Even N: the average of the two middle values, (Y(N/2) + Y(N/2+1))/2. |
| What the word "average" means | NIST uses average as a synonym for the mean. The U.S. Census Bureau labels it "Mean (average) income". | Not what NIST means by average. The Census Bureau publishes it as a separate statistic, "Median income". |
| Effect of extreme values | Extreme values in the tails distort it. | Not distorted by extreme values, because the median is based on ranks. |
| Symmetric data | For a normal distribution the mean, median and mode are equivalent, so the mean is a reasonable location estimate. | Gives about the same value as the mean (NIST sample of 10,000 normal values: mean 0.005, median -0.010). |
| Skewed data | Pulled in the direction of the skew: above the median when the right tail is heavier, below it when the left tail is heavier. NIST exponential sample: 1.001. | Stays nearer the bulk of the data. NIST exponential sample: 0.684. NIST lognormal sample: mean 1.677, median 0.989. |
| Heavy-tailed data | Can be useless as a typical value. NIST Cauchy sample: mean 3.70, well above the vast majority of the data. | Still a useful typical value. NIST Cauchy sample: median -0.016. |
| Worked example (illustrative, computed here) | Values 30, 32, 35, 38, 215: sum 350, divided by 5 gives 70. One large value pulls it above four of the five values. | Same values, already sorted: the middle value is 35. Replacing 215 with 2,150 would not change it. With 2, 4, 6, 8 (even N) the median is (4 + 6) / 2 = 5. |
| Official statistics | The Census Bureau defines mean income as total aggregate income of a group divided by the number of units in that group. | The Census Bureau defines median income as the amount that divides the income distribution into two equal groups. Its headline figure is a median: median household income was $83,730 in 2024. |
| When to pick each | Data well approximated by a normal distribution (check a histogram or normal probability plot), where NIST says the mean is a reasonable estimator. Also when the total matters, as in aggregate income divided by number of units. | Data with extreme values in the tails, where NIST says the median is a better location estimate. For skewed data NIST says all the measures are useful, so report both and say which is which. |
| Source | NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1 Measures of Location (https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm), read 2026-10-29. | U.S. Census Bureau, CPS subject definitions (https://www.census.gov/programs-surveys/cps/technical-documentation/subject-definitions.html) and Income in the United States: 2024, P60-286 (https://www.census.gov/library/publications/2025/demo/p60-286.html), read 2026-10-29. |
Common questions
Common questions about Average (mean) vs Median
Is the average the mean or the median?
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NIST uses average as a synonym for the mean, the sum of the data points divided by their number. The median is a different statistic, so a figure called an average should be read as a mean unless the source says otherwise. The Census Bureau publishes "Mean (average) income" and "Median income" as two separately defined measures.
When should I use the median instead of the mean?
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When the data have extreme values in the tails. NIST states that such values distort the mean but not the median, since the median is based on ranks, and that in general the median is the better location estimate for such data.
Can the mean and the median be the same?
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Yes. For a normal distribution NIST says the mean, median and mode are equivalent. In a skewed distribution they differ, and the mean is pulled toward the longer tail.
What is the difference between median and average for skewed data?
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The mean is pulled in the direction of the skew, so it exceeds the median when the right tail is heavier and falls below it when the left tail is heavier. NIST says that for skewed distributions the mean, median and mode are all useful, so reporting more than one is reasonable.
Going deeper
