Math

Statistics Calculator — Free 2026

Calculate mean, median, mode, standard deviation, variance, and more from any set of numbers.

Enter Numbers (comma, space, or newline separated) Please enter at least one valid number.

Results

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Mean

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Median

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Mode

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Range

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Variance (Pop.)

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Std Deviation (Pop.)

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Min

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Max

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Count

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Sum

How It Works

Enter your data
View all statistics
Interpret the results

Understanding Descriptive Statistics

Descriptive statistics summarize and organize the characteristics of a dataset. They provide a quick overview that helps you understand the shape, center, and spread of your data without examining every individual value. The most important descriptive statistics fall into two categories: measures of central tendency (mean, median, mode) that tell you where the "middle" of the data lies, and measures of dispersion (range, variance, standard deviation) that tell you how spread out the values are.

Measures of Central Tendency

The mean (arithmetic average) is the most commonly used measure — simply add all values and divide by the count. It is sensitive to outliers, so a single extreme value can pull the mean significantly. The median (middle value in sorted data) is more robust against outliers and is often preferred for income data, housing prices, and other skewed distributions. The mode (most frequent value) is useful for categorical data and for identifying peaks in a distribution. For a focused analysis of spread, use our standard deviation calculator which includes step-by-step calculations.

Measures of Dispersion

Range is the simplest measure of spread — just the difference between the maximum and minimum values. While easy to compute, it only considers two data points and is heavily influenced by outliers. Variance measures the average squared distance from the mean, giving more weight to values far from the center. Standard deviation is the square root of variance and is expressed in the same units as the data, making it more interpretable. In a normal distribution, about 68% of values fall within one standard deviation of the mean, and 95% within two standard deviations.

When to Use Each Statistic

Use the mean when data is roughly symmetric without extreme outliers. Use the median for skewed data or when outliers are present. Use mode for categorical data or to find the most common value. Standard deviation is the go-to measure for spread in most analyses, while range gives a quick but rough picture. For percentage-based comparisons, try our percentage calculator.

Frequently Asked Questions

What is the difference between mean, median, and mode?

The mean is the arithmetic average (sum divided by count). The median is the middle value when data is sorted — it splits the dataset in half. The mode is the most frequently occurring value. For symmetric distributions these three are similar, but for skewed data they can differ significantly.

What is standard deviation?

Standard deviation measures how spread out the values in a dataset are from the mean. A low standard deviation means values cluster close to the mean, while a high standard deviation indicates values are spread over a wider range. It is the square root of the variance.

What is the difference between population and sample variance?

Population variance divides the sum of squared deviations by N (total count), while sample variance divides by N-1 (Bessel's correction). Use population variance when you have data for the entire group, and sample variance when working with a subset. This calculator uses population formulas by default.

How do I enter my data?

Enter numbers separated by commas, spaces, or newlines. The calculator automatically parses your input and ignores any non-numeric text. You can paste data directly from spreadsheets or other sources.