Basic Statistics Calculator
From a list of numbers, compute mean, median, mode, min, max, sum, standard deviation and variance (population and sample). Everything in your browser.
Descriptive statistics: summarizing data
Descriptive statistics boil a dataset down to a few numbers: measures of central tendency (mean, median, mode), of dispersion (min, max, range = max − min, variance, standard deviation), and of shape (skewness, kurtosis). The coefficient of variation CV = σ / μ is dimensionless, which is what lets you compare dispersion across populations measured on different scales. The split between population and sample variance comes down to the denominator. The population formula is σ² = Σ(xᵢ − μ)² / N, while the sample one is s² = Σ(xᵢ − x̄)² / (n − 1); Bessel's correction divides by n − 1 so that s² stays an unbiased estimator. Run [2, 4, 4, 4, 5, 5, 7, 9] through it and you get mean 5, median 4.5, mode 4, sample s ≈ 2.14.
Applications
Scientific research leans on it, and so does exploratory data analysis (EDA), the thing you do before fitting any model — usually a quick pandas.describe() or R's summary(). From there it spreads into sample planning, quality control (process capability), market research, and the KPIs that fill reports.
FAQ
Population or sample variance? Go with population when your data is the whole thing — every employee at the company, for instance. Switch to the sample version (n − 1) when you only have a subset and want to infer something about the larger population. That's Bessel's correction doing its job.
What does the coefficient of variation tell me? It captures dispersion relative to the mean. A CV of 10% says the standard deviation is one tenth of the mean. Once you cross CV > 30% you're looking at high variability. Just remember the measure breaks down when the mean sits close to zero.
Mean or median? Outliers drag the mean around, whereas the median barely budges. With skewed distributions like income or real estate prices, the median paints the typical case far more honestly. Brazilian household income is the textbook example of this.
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Descriptive statistics of a list
When a list of numbers shows up, the opening questions almost always repeat. What's the average? The middle value? How much do they swing? The calculator answers all of it at once, running the full descriptive statistics of the set you paste.
Out come mean, median, mode, minimum, maximum and sum. Out come the standard deviation and variance too, these in both versions, population and sample, a distinction that weighs in academic work. Anyone studying statistics, analysing experiment data or simply trying to make sense of a handful of measurements finds what they need here.
The data never leaves the browser, since it's all worked out right here. Paste the numbers separated by comma, space or line break and the metrics appear all at once.