Statistics Calculator

Core statistics formulas

Descriptive statistics summarize a list of numbers. The mean formula is mean = sum of values ÷ count. The median is the middle value after sorting, or the average of the two middle values when there is an even count. The range is maximum − minimum. The mode is the value or values that appear most often. This calculator parses numbers separated by commas, spaces, tabs or new lines and updates all of those summaries at once.

Spread is measured with variance and standard deviation. Population variance is Σ(x − mean)² ÷ n, where n is the count. Population standard deviation is the square root of that variance. Use population formulas when your list contains every value you care about, such as all scores in one class or all sales in a small report.

Population versus sample

Sample variance uses Σ(x − mean)² ÷ (n − 1). Dividing by n − 1 corrects the tendency of a sample to underestimate the variation of the larger population it represents. Sample standard deviation is the square root of sample variance. If you are analyzing a survey, experiment sample or subset of a larger dataset, the sample values are usually the better choice. If there is only one value, sample variance is not defined, so the calculator shows a dash for sample spread.

Input and privacy notes

Non-number text is ignored, so you can paste simple columns or comma-separated values. Check that decimal separators match your browser language and that negative signs are included where needed. Results use ordinary JavaScript number precision, which is fine for everyday statistics but not a replacement for audited statistical software. The pasted data never leaves your browser and is not stored by the page.

Worked example

Using the sample list 12, 15, 15, 18, 20, 22, 25: the sum is 127 and the count is 7, so the mean is about 18.14. The median is 18, the mode is 15 and the range is 25 − 12 = 13. The population variance is about 17.55 with a standard deviation of 4.19, while the sample variance is about 20.48 with a standard deviation of 4.53.

Keep outliers in mind when choosing a summary. One extreme value pulls the mean toward it but barely moves the median, so compare the two when a list looks skewed. If no value repeats, the mode is shown as “No repeat”. Because commas and spaces both separate numbers, type decimals with a point: 1,5 is read as the two values 1 and 5, not as one and a half.