Statistics
Mean vs Median
Both describe 'the middle' of data — but outliers make them very different numbers.
Mean
Sum divided by count — sensitive to outliers
Median
The middle value — resistant to outliers
At a glance
| Mean | Median | |
|---|---|---|
| Formula | Sum ÷ count | Middle value when sorted |
| Effect of outliers | Pulled strongly toward extremes | Largely unaffected |
| Best for symmetric data | Yes — accurate center | Yes, but mean is more informative |
| Best for skewed data | Often misleading | Better represents typical value |
| Used for income/prices | Inflated by high earners | Better represents typical household |
| Used for test scores | Usually appropriate | More robust if score distribution is skewed |
Pick Mean
Symmetric distributions without extreme outliers — standardized test scores, heights, manufacturing tolerances, or any data where values cluster reasonably around the center. Mean is more sensitive and statistically useful in these cases.
Pick Median
Skewed data with outliers — income, home prices, response times, wealth, or anything with a long tail in one direction. Median represents what is typical rather than what is average when a few extreme values distort the mean.
How one billionaire skews the mean — a worked example
Suppose you survey income in a small town of 10 people:
$32,000 / $35,000 / $38,000 / $41,000 / $43,000 / $44,000 / $47,000 / $52,000 / $55,000 / $60,000
Mean: sum = $447,000; mean = $44,700. This accurately reflects the typical earner here. Median: middle two values are $43,000 and $44,000; median = $43,500. Very close to the mean because the data is roughly symmetric.
Now suppose a tech billionaire moves to town. His income is $2,000,000,000 ($2 billion).
New mean: ($447,000 + $2,000,000,000) ÷ 11 = ~$182 million. Every resident now has an "average income" of $182 million — a number that describes exactly zero of the actual residents.
New median: the middle value (6th of 11, sorted) is $44,000. Nearly unchanged.
This is the famous problem with mean income statistics. The mean household income in the United States is substantially higher than the median household income precisely because a small number of extremely high earners pull the mean upward. The median tells you what a typical household actually earns.
When median is misleading too — bimodal distributions
The median is not universally superior — it can also mislead in certain situations.
The classic case is a bimodal distribution: data with two distinct clusters. Imagine a town where half the residents earn $25,000 and half earn $85,000, with almost no one in between.
Mean: ($25,000 + $85,000) ÷ 2 = $55,000 Median: $55,000 (the midpoint between the two groups)
Both numbers give you $55,000 — a value that describes almost no one in the actual population. Here, neither mean nor median is useful without also knowing that the distribution is bimodal.
Other cases where the median can mislead: - Very small datasets: With 5 data points, the median is just a single value with high sampling variance. - Discrete data with many ties: The median of exam scores where 60% of students score exactly 70 is 70 — a real number, but one that masks the distribution. - When you care about totals: Mean matters when summing. If you want to know total payroll, the mean salary matters more than the median salary.
The practical lesson: always look at the distribution, not just a single summary statistic. When in doubt, report both mean and median — if they are close, the data is roughly symmetric and either works. If they diverge, you have skew or outliers that are worth understanding.
A practical guide to choosing
Use the mean when: - The data is roughly symmetric (a histogram would look bell-shaped) - There are no extreme outliers, or outliers represent real and relevant data - You need the result for further mathematical operations (mean is mathematically tractable in ways median is not) - You are measuring things like test scores, heights, temperatures, manufacturing dimensions
Use the median when: - The data is skewed (income, wealth, home prices, response times, wait times) - There are outliers that could distort a typical-value interpretation - You want to say "half of people/things are above this value and half are below" - You are reporting real estate prices, salary benchmarks, or any metric where a few extreme values would make the average misleading
Report both when: - You want to be transparent about the data shape — a large gap between mean and median is itself informative - Your audience includes both people who want the optimistic/pessimistic summary and those who want the typical value
A useful rule of thumb: if someone asks "what does the typical person experience?" use the median. If someone asks "what is the total divided by the number of people?" that is definitionally the mean.
For quick calculations, our percentage calculator handles the arithmetic once you have your numbers.