Mean, Median & Mode Calculator
Paste a list of numbers and get the mean, median, mode, range, standard deviation and more.
Written by Rahman · Last reviewed
Quick answer
Mean is the sum divided by the count, median is the middle value of the sorted list, and mode is the most frequent value. The mean is pulled by outliers and the median is not, which is why income is normally reported as a median. Standard deviation measures how far values typically sit from the mean; this calculator defaults to the sample formula, √(Σ(xᵢ − mean)² ÷ (n − 1)), with population (÷ n) available as a toggle.
Use the sample basis when your numbers are a subset drawn from a larger group, which is what most coursework and most real datasets are. Use the population basis only when the numbers are the entire group. Quartiles are interpolated the way spreadsheets do it, so they match Excel and Google Sheets.
Results are estimates for general guidance only. Double-check any figure you rely on for an important decision.
About the Mean, Median & Mode Calculator
Mean, median and mode are the three classic measures of central tendency in statistics. Each tells you something slightly different about a dataset. The mean (average) is sensitive to outliers; the median (middle value) ignores them; the mode (most frequent value) highlights repetition.
This calculator also returns the range, standard deviation, sum, count, minimum and maximum, covering everything a student, analyst or curious user typically needs for a quick statistical summary.
Mean = sum / count · Median = middle value of sorted list · Mode = most frequent value Standard deviation (sample, default) = √(Σ(xᵢ − mean)² / (n − 1)) · Standard deviation (population) = √(Σ(xᵢ − mean)² / n)
Mode returns "No mode" when every value appears the same number of times.
When the mean stops describing the data
The mean is the average most people reach for, and it is the one most easily distorted. Because every value contributes in proportion to its size, a single extreme figure pulls it away from the bulk of the data, and the result is a number that no longer describes anything typical.
Take five salaries of 25,000, 30,000, 35,000, 40,000 and 500,000. The mean is 126,000 and the median is 35,000. Four of the five people earn less than the mean, so quoting it as the average salary describes nobody in the set. The median is unaffected by how extreme the outlier is, because it only cares about position.
- Income, house prices and wealth are all right-skewed, which is why they are almost always reported as medians.
- A large gap between mean and median is itself informative: it signals skew, and which side is larger tells you which direction.
- Symmetric data has a mean and median close together, and there the mean is the better summary because it uses every value.
What each measure is actually for
The three measures answer different questions rather than competing to answer the same one. The mean is the balance point and the right input for totals: average spend times customer count gives revenue, which the median cannot do. The median is the middle value and the right summary for a typical case in skewed data. The mode is the most frequent value, and the only one that works on categories rather than numbers.
Spread matters as much as the centre. Two datasets can share a mean of 50 while one ranges from 48 to 52 and the other from 0 to 100, and no measure of central tendency distinguishes them. That is what standard deviation is for.
- Mode is the only one of the three that applies to non-numeric data such as most common colour or most frequent response.
- A dataset can have no mode, one mode, or several; the calculator reports "No mode" when every value appears equally often.
- Before removing an outlier, establish whether it is an error or a real observation. Genuine extremes often carry the most important information in the set.
Frequently Asked Questions
When should I use the median instead of the mean?
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Use the median for data with outliers or skewed distributions: incomes, house prices, response times. The mean is fine for symmetric data like exam scores or measured heights.
What does standard deviation tell me?
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How spread out the data is from the mean. A small standard deviation means values cluster tightly; a large one means they are widely spread. In a normal distribution, ~68% of values lie within one standard deviation of the mean.
Can a dataset have more than one mode?
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Yes. A "bimodal" distribution has two equally-frequent values. The calculator returns all values tied for the highest frequency.
Sample or population standard deviation: which does this use?
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Sample (dividing by n − 1) is the default, since most real-world datasets are a sample of a larger population rather than the whole thing: a survey of 200 shoppers, not every shopper who exists. Switch to population (dividing by n) if your data genuinely is the entire population, not a sample drawn from it.