Descriptive statistics
Mean, Median and Mode Calculator
The three measures of centre, side by side, with the gap between them explained.
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How to read this result
Mean, median and mode answer the same question three ways. The mean is the balance point. The median is the middle. The mode is the most common value. On symmetric data they coincide; the more skewed the data, the further apart they drift.
The gap is the finding. Mean above median means a long right tail; mean below median means a long left tail. That single comparison tells you more about the shape than skewness does, and takes no arithmetic.
Which one to report depends on what you will do with it. The mean is the only one that adds up: mean × n gives the total, which is why payroll and revenue use it. The median is the one that survives outliers, which is why house prices and incomes use it. The mode is the only one that works on categories, and the only one that can be missing or multiple.
A mode is not always meaningful. With continuous measurements, every value tends to be unique and there is no mode at all — which is what the calculator will say rather than inventing one.
The formula
The mean. The median is the middle value once sorted — or the average of the two middle values when n is even. The mode is the value with the highest frequency, and there may be none or several.
Worked example
Ten salaries, one of them a founder's
Ten salaries at a small company: 32,000, 35,000, 36,000, 38,000, 41,000, 42,000, 45,000, 48,000, 52,000 and 240,000. What is a typical salary here?
- Add them and divide by ten.609,000 / 10 = 60,900
- Sort them and take the middle two, then average.41,000 and 42,000 → 41,500
- No value repeats, so there is no mode.no mode
- Compare the two centres.the mean is 19,400 higher than the median
Nine of the ten people earn less than the mean. That is the whole argument for the median: “average salary 60,900” is arithmetically true and describes nobody in this company.
Checked against R's mean and median.
The calculator above is loaded with these numbers by the Load the worked example button.
Assumptions, and when to use something else
The mean requires numbers you can meaningfully add. The median requires values you can order. The mode requires nothing at all — it works on colours, brands and survey categories.
That hierarchy is the reason all three exist. A five-point satisfaction scale can be reported as a median or a mode without controversy; reporting its mean assumes the distance from 1 to 2 equals the distance from 4 to 5, which is a real assumption rather than a technicality.
- You want the spread as wellDescriptive statisticsEvery summary statistic at once, with a histogram.
- The data are growth rates or ratiosGeometric meanRates multiply rather than add, so they must be averaged geometrically.
- Some values should count more than othersWeighted averageFor grades, portfolios and any average where the items are not equally important.
- One value is distorting the meanOutlier detectionIdentify it, decide what it is, and see the summary with and without it.
Questions people ask
When should I use the median instead of the mean?
Whenever the data are skewed or contain outliers — incomes, house prices, waiting times, response times. The median answers “what does a typical case look like”, which is usually the question being asked.
Can a data set have more than one mode?
Yes. Two values tied for most frequent make the data bimodal, and the calculator lists both. Genuinely bimodal data usually means two populations are mixed together, which is worth knowing before you summarise them as one.
What is the mode when every value appears once?
There is no mode. Some textbooks say every value is a mode, which amounts to the same thing: the mode carries no information here. This is the normal situation for continuous measurements.
How do I find the mean of grouped data?
Multiply each class midpoint by its frequency, add those products, and divide by the total frequency. The frequency table calculator builds the grouped table with midpoints; the result is an approximation, because the original values inside each class are gone.