Statistics Calculator

Find the mean, median, mode, range, variance, standard deviation and quartiles for any list of numbers.

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How These Are Calculated

Mean is the sum divided by the count. Median is the middle value of the sorted data (or the average of the two middle values for an even count). Mode is the most frequent value. Variance is the average squared deviation from the mean, and standard deviation is its square root - both are shown for population (divide by N) and sample (divide by N-1) formulas.

When to Use Which
  • Use mean for a general average when there are no extreme outliers
  • Use median when your data has outliers or is skewed
  • Use mode for the most common category or value
  • Use sample standard deviation when your data is a subset of a larger population
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Frequently Asked Questions

The mean is the sum of all values divided by how many there are (the arithmetic average). The median is the middle value when the numbers are sorted in order. The mode is the value (or values) that appear most often. Mean is sensitive to outliers, while median is not - which is why median is often used for figures like household income.

Population standard deviation is used when your data represents the entire group you care about, and divides by N. Sample standard deviation is used when your data is a sample drawn from a larger population, and divides by N-1 (Bessel's correction), which gives a slightly larger, less biased estimate. This calculator shows both.

Quartiles split sorted data into four equal parts. Q1 (the lower quartile) is the median of the lower half, Q3 (the upper quartile) is the median of the upper half, and the interquartile range (IQR = Q3 - Q1) measures the spread of the middle 50% of your data, which is useful for identifying outliers.

Yes. If two or more values tie for the highest frequency, the data set is multimodal and all of the tied values are shown as modes. If every value appears exactly once, the data set has no mode.

Enter numbers separated by commas, spaces, new lines, or a mix of these. Negative numbers and decimals are supported.