The median is not sensitive to outliers. It is one of the most resistant measures of central tendency in statistics, meaning extreme values at either end of your data have little to no effect on it. While the mean shifts every time you add or change a value, the median stays anchored to the middle position of your dataset regardless of how extreme the highest or lowest values become.
Why the Median Resists Outliers
The median is simply the middle value when all observations are arranged in order. Because it depends on position rather than magnitude, it doesn’t matter whether the largest number in your dataset is 100 or 100 million. The middle value stays the same either way.
Statisticians quantify this property using something called the breakdown point: the fraction of data points that would need to be replaced with extreme values before the statistic becomes meaningless. The mean has a breakdown point that approaches zero, meaning a single wildly extreme value can distort it. The median has a breakdown point of 0.5, the highest possible. You would need to corrupt nearly half the data before the median breaks down. That makes it the gold standard for outlier resistance among simple summary statistics.
Mean vs. Median With Skewed Data
The difference between the mean and median becomes obvious when data is skewed or contains extreme values. Consider a set of home prices: $450,000, $475,000, $490,000, $509,000, $525,000, $540,000, and $1,200,000. The median here is $509,000, which sits right in the middle and represents a typical home in the dataset. The mean gets pulled upward by that $1.2 million property, landing well above most of the actual prices.
In real estate data with just a couple of high-end outliers, the average can land above 80% of the actual data points, making it a poor representation of a “typical” value. This is why housing reports almost always use median prices. The median protects against the reality that datasets are rarely as clean as you’d want them to be.
The same logic applies to income data. Because a small number of extremely high earners pull the mean upward, the median household income is consistently thousands of dollars lower than the mean. Economists and government agencies prefer the median when describing what a typical household actually earns, because it reflects the middle of the distribution rather than being inflated by billionaires at the top.
Where the Median Has Limitations
Resistance to outliers sounds like a pure advantage, but it comes with a trade-off. The median ignores most of the information in your data. It only cares about the middle value (or the two middle values in an even-numbered set), so it throws away everything the other data points could tell you about the overall distribution. Statisticians describe this as lower “efficiency,” meaning the median needs a larger sample to achieve the same precision as the mean when your data is well-behaved and outlier-free.
With very small samples, the median’s behavior can also feel less intuitive. In a sample of just three observations, the median is literally the single middle value. If that middle value happens to be unusual, your entire summary rests on one data point. The resistance property still holds in a technical sense (changing the highest or lowest value won’t move it), but with so few observations, no summary statistic is especially reliable.
The Trimmed Mean as a Middle Ground
If you want something between the sensitivity of the mean and the resistance of the median, the trimmed mean offers a compromise. It works by removing a fixed percentage of the highest and lowest values before calculating the average of what remains. A 10% trimmed mean, for instance, drops the top and bottom 10% of observations.
This approach is more resistant to outliers than the ordinary mean while using more of the data than the median does. According to NIST, the trimmed mean provides a location measure that is more resistant than the mean but has greater statistical efficiency than the median. Its breakdown point equals whatever trimming percentage you choose: a 20% trimmed mean can withstand up to 20% contamination. The median is essentially a trimmed mean taken to its extreme, where you trim everything except the center.
When to Use the Median Over the Mean
The median is the better choice whenever your data is skewed in one direction or contains values that are far removed from the bulk of the observations. Real estate prices, household incomes, hospital wait times, and company revenues all tend to have long tails on one side, making the median a more honest summary of the typical case.
The mean is preferable when your data is roughly symmetric, free of extreme values, and you want maximum statistical precision. It’s also necessary for many downstream calculations (standard deviation, for example, depends on the mean). In practice, comparing the mean and median is itself a quick diagnostic: a large gap between the two signals that outliers or skewness are present and that the median is likely the more trustworthy number.