Calculate average (mean), middle value (median), and most common value (mode).
Enter values to see the result.
Mean: sum of all values / number of elements
Median: middle value of sorted data
Mode: most frequently occurring value
Guide: Mean, Median, and Mode
The arithmetic mean is the most commonly used measure of central tendency, calculated by summing all values and dividing by their count. It works best for data that is symmetrically distributed without extreme outliers. When data clusters around the mean, it provides a complete picture of the typical value.
The median is the value that divides the dataset into two equal halves - half the values are smaller, half are larger than the median. It is resistant to outliers, making it ideal for data with extreme values or skewed distributions. It is commonly used for income, real estate prices, and other economic data.
The mode is the most frequently occurring value in a dataset. It is useful for identifying the most popular category or option. When all values are unique, there is no mode - such a distribution is called amodal.
When to use which: Use the mean for symmetric data without outliers. Use the median for skewed data or data with extreme values. Use the mode for categorical data or when you want to know the most common response.
One outlier moves the mean by 44.6 and the median by exactly zero
Ten salaries averaging 40 have a median of 39 — the two agree closely, as they do for most well-behaved data. Replace the top earner with 500 and the mean jumps to 84.6 while the median does not move at all. The mean is now above nine of the ten people it describes, which is the moment an average stops describing anything.
How it works
- Calculates the mean, median, mode and range of a set of values.
- Shows all three together, because the gap between them is what tells you the shape of the data.
- Handles multiple modes and even-sized sets, where the median is the midpoint of the middle pair.
mean = sum ÷ count moves with every value median = the middle value once sorted moves only with the middle mode = the most frequent value may not exist, or may be several mean far above median → a long tail to the right mean ≈ median → roughly symmetric
Worked example
Ten salaries, then the same ten with one changed.
- 30, 32, 35, 36, 38, 40, 42, 45, 48, 54
- mean 40.0, median 39.0 — close together
- replace 54 with 500
- mean 84.6, median 39.0
- 9 of the 10 values now sit below the mean
The mean moved 44.6 and the median moved 0.0. Reporting the average alone would describe this group as earning 84.6 when nine of them earn less than half that. The median is not more correct in general — it is more robust, which is a different property and the one that matters here.
Reading the result
- Income, house prices, waiting times and file sizes all have long right tails, so the mean sits above the median as a rule. This is why national statistics report median household income: the mean answers a question almost nobody is asking.
- The mean is still the right choice when every value should count equally — totals, budgets, anything you will multiply back up by the count. Use the median when you want a typical case and the tail is not the point.
- Mode is the only one that works on categories rather than numbers. It is also the least stable: a set can have no mode, one, or several, and adding a single observation can change the answer entirely.
- When mean and median differ sharply, that gap is itself the finding. Report both rather than choosing, because the difference tells the reader the distribution is skewed and a single number will not represent it.
Common questions
- Which average should I use?
- Compare them first. If mean and median are close, either works. If they diverge, the data has a tail, and the median describes a typical case while the mean describes the total divided up. Neither is wrong; they answer different questions.
- Why is the average salary higher than what most people earn?
- Because a small number of very high earners pull the mean up while leaving the median untouched. In the example above, the mean exceeds what nine of the ten people earn — the average is real arithmetic and still a poor description of the group.