Statistics Calculator (Mean, Median, Variance, Standard Deviation, Quartiles)
Paste a list of numbers separated by commas, spaces, or line breaks to instantly get the mean, median, mode, range, variance and standard deviation (both population and sample), quartiles (Q1-Q3), a frequency table, and a histogram.
Tips
- You can separate values with commas, spaces, or line breaks in any combination — pasting a column straight from a spreadsheet is recognized correctly too.
- Sample standard deviation (the unbiased variance divided by n − 1) is used when your data is a sample drawn from a larger population rather than the whole population itself. If you have data for every member of the population, use the population variance instead.
- The interquartile range (IQR) is far less sensitive to outliers than the mean or the range, making it a more robust measure of spread for messy real-world data.
- If multiple values tie for the highest frequency, all of them are shown as the mode. If every value occurs exactly once, the result shows "no mode."
- The number of histogram bins is chosen automatically with Sturges' formula (based on the sample size), so larger datasets get finer-grained bins.
Frequently Asked Questions
Side Note — When was the term "standard deviation" coined?
The statistician Karl Pearson is credited with coining the term "standard deviation" in an 1893 paper, giving a single name to a concept — essentially the square root of a mean squared error — that had previously been referred to inconsistently. Pearson was one of the founders of modern descriptive statistics, and his name also lives on in the Pearson correlation coefficient and the chi-squared test.
Whether to divide the sum of squared deviations by n or by n − 1 is a key question for understanding the difference between a "sample" and a "population" in statistics. Because computing variance from a sample mean tends to slightly underestimate the true population variance (a loss of one degree of freedom), dividing by n − 1 instead yields an unbiased estimator when inferring a population's spread from a sample. This correction is attributed to Ronald Fisher, whose work profoundly shaped statistics in the early 20th century.
Quartiles and the box plot were popularized by the American statistician John Tukey. In the 1970s he championed "exploratory data analysis," an approach that emphasizes getting a rough, hands-on feel for the shape of data before reaching for complex formulas. Box plots remain a go-to tool for visualizing outliers today.