Ask ten people for "the average" of a dataset and you may get three correct answers. Mean, median, and mode are all measures of central tendency — but they measure central tendency in very different ways. Using the wrong one can mislead decisions, distort headlines, and hide real patterns in the data.
The three averages, defined
The mean is the arithmetic average: add every value, divide by the number of values. It is what most people mean by "average."
The median is the middle value when the data is sorted in order. If there are an even number of values, the median is the average of the two middle ones.
The mode is the value that appears most often. A dataset can have one mode, multiple modes, or no mode at all.
A simple example
Consider seven salaries (in thousands): 40, 42, 45, 48, 50, 52, 300.
- Mean: (40 + 42 + 45 + 48 + 50 + 52 + 300) ÷ 7 = 82.4
- Median: sorted, the middle value is 48
- Mode: none — no value repeats
The mean says the "average" salary is $82,400. The median says $48,000. Which feels right? Six of seven people earn under $53,000. The mean was pulled upward by one outlier. In skewed data, the median is often the more honest summary.
When the mean is best
Use the mean for roughly symmetric data with no extreme outliers — test scores in a well-designed exam, heights in a population, daily temperatures over a stable month. The mean uses every data point, so it is statistically efficient when the data behaves itself.
The mean is also the right choice when you need a total. Mean daily revenue × 30 days = monthly revenue. Median revenue × 30 days means nothing.
When the median is best
Use the median for skewed data or data with outliers. Income, home prices, wait times, web page load times, and response times all tend to have long right tails — a few very large values that drag the mean upward. The median resists this distortion.
This is why the US Census Bureau leads with median household income (it publishes the mean as well). And why "average home price" reporters usually cite the median. A handful of billionaires would make the mean income look like everyone is rich.
When the mode is best
Use the mode for categorical data where "adding" makes no sense. The most common blood type. The most frequently ordered menu item. The most popular car color. Mean eye color is not a thing; mode eye color is.
Mode is also useful for discrete numeric data with clear peaks — shoe sizes sold in a store, for instance. The mode tells inventory managers what to stock most of.
How outliers change the picture
Take the list 2, 3, 4, 5, 6. Mean and median are both 4. Now add a 100: 2, 3, 4, 5, 6, 100. Mean jumps to 20. Median barely moves (to 4.5). The mean became five times larger because of one value. The median shrugged.
Outliers deserve investigation, not just removal. Sometimes they are data errors. Sometimes they are the most important points in the dataset (fraud detection, anomaly spotting). Know what your outlier is before you decide what to do with it.
Skew and what it tells you
If mean > median, the data is often right-skewed (long tail on the high side). Examples: income, house prices, city populations.
If mean < median, the data is often left-skewed (long tail on the low side). Examples: test scores with a ceiling effect, age at retirement.
If mean ≈ median, the data may be roughly symmetric, but not necessarily: the list 1, 4, 4, 5, 6 has a mean and a median of 4, yet its long tail is on the low side. Equal mean and median also do not make data normal.
Comparing mean to median is a quick skew check that takes two seconds, but treat it as a rule of thumb, not a test. It fails surprisingly often, especially with discrete data such as counts. For example, a Poisson distribution with a mean of 0.75 is right-skewed, yet its median is 1, above the mean. When it matters, look at a histogram.
Multiple modes and bimodal distributions
Some data has two peaks. The waiting times between eruptions of Old Faithful geyser in Yellowstone are a good example: the National Park Service gives two typical intervals, a shorter one and a longer one, because the wait depends on how long the previous eruption lasted. Reporting a single mean here hides the structure. Bimodal data suggests two underlying groups mixed together — often worth separating before analysis.
Beyond the three averages
For extreme outliers, consider the trimmed mean: chop off the top and bottom 5% or 10% and average what remains. Olympic judging uses this. So does scientific data cleaning.
For growth rates and investment returns, use the geometric mean of the growth factors, not of the percentages themselves: turn each return into a factor (+10% becomes 1.10, −5% becomes 0.95), take the n-th root of their product, and subtract 1. Returns of +10% and +20% average about 14.89% a year this way, not the 15% the arithmetic mean suggests. For rates such as speeds over equal distances, use the harmonic mean instead: 60 miles at 30 mph plus 60 miles at 60 mph averages 40 mph, not 45.
Run the numbers
Our statistics calculator computes mean, median, mode, standard deviation, and more from any list of values you paste in. Use it to sanity-check your data before choosing which "average" to quote. Picking the right statistic is half the battle; the other half is explaining why you picked it.