Mean · Standard Deviation Calculator
One list of numbers, all the statistics
Statistics
Formula Summary
| Statistic | Formula | Meaning |
|---|---|---|
| Mean (x̄) | Σx ÷ n | Sum divided by count |
| Median | middle of sorted values | Average of middle two if n is even |
| Variance (population σ²) | Σ(x−x̄)² ÷ n | Mean squared deviation |
| Variance (sample s²) | Σ(x−x̄)² ÷ (n−1) | Estimating a population from a sample |
| Standard deviation | √variance | Spread in the data's own units |
FAQ
What is the difference between variance and standard deviation?
Variance is the mean of squared deviations (squared units); standard deviation is its square root, back in the data's own units — the one you usually interpret.
When do I divide by n vs n−1?
Use n when your data is the whole population; use n−1 when it's a sample used to estimate a population. Both values are shown.
When is the median better than the mean?
With skewed data or outliers (like incomes), the mean gets pulled toward extremes — the median better represents a typical value.
Can there be more than one mode?
Yes — every value tied for most frequent is a mode. If nothing repeats, there is no mode.
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