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These are the core measures of descriptive statistics — each tells you something different about your data. Together they give a complete picture of any dataset at a glance.
The mean is the sum of all values divided by the count. It's the most familiar measure of "typical" — but it's sensitive to outliers. One unusually large or small value can drag the mean far from where most of your data sits. If your mean and median are notably different, an outlier is likely the cause.
Sort your numbers from lowest to highest; the median is the one in the middle (or the average of the two middle values if there's an even count). Because it ignores the extremes entirely, it's a better measure of central tendency for skewed data — household incomes, house prices, and wait times are classic examples where median is more meaningful than mean.
The mode is whichever value appears most often in your dataset. A dataset can have no mode (all values unique), one mode, or multiple modes. It's most useful for discrete data — exam scores, survey ratings, shoe sizes — rather than continuous measurements where repetition is rare.
Standard deviation measures how spread out your values are around the mean. A low standard deviation means values cluster tightly; a high one means they're scattered widely.
Use population standard deviation when your numbers are the entire group you care about — every student in a class, every product in a batch. Use sample standard deviation when your numbers are a sample drawn from a larger group and you want to estimate the whole group's spread. The sample version divides by (n − 1) instead of n, which corrects for the tendency of a small sample to underestimate the true spread.
Variance is simply standard deviation squared. It's less intuitive than standard deviation (because the units are squared too — square metres instead of metres, for example) but is the form used in many statistical formulae. This calculator shows both population and sample variance alongside their standard deviations.
When the mean is higher than the median, a few large values are pulling the average up — the data is right-skewed. When the mean is lower, a few small values pull it down — left-skewed. The interpretation note below your results flags this automatically.
The range is the simplest spread measure: maximum minus minimum. It tells you the full span of your data but nothing about how values are distributed within that span. Two datasets can have the same range with completely different shapes — one tightly packed around the middle, another scattered evenly from end to end. Combine it with standard deviation for a more complete picture.