Free Descriptive Statistics Calculators

Understanding Data Spread

The mean tells you where the center of your data lies. Standard deviation tells you how spread out the data is around that center. Together, these two numbers summarize a dataset more informatively than any single data point can.

Standard Deviation Calculator

Paste or type your data values and the calculator returns sample standard deviation (s), population standard deviation (σ), variance, mean, median, mode, range, and count. It uses the correct formula for each — dividing by n−1 for samples and n for populations.

Sample vs. Population

If your data represents an entire population, use population standard deviation. If it is a sample from a larger population, use sample standard deviation (with Bessel's correction, n−1). Our calculator displays both.

Key Descriptive Measures

• Mean — Arithmetic average. Sensitive to outliers.
• Median — Middle value when sorted. More robust to outliers than the mean.
• Standard Deviation — Average distance from the mean. Low SD = tightly clustered; high SD = widely spread.
• Variance — SD squared. Useful in formulas but harder to interpret since units are squared.

Applications

Quality engineers set tolerance limits. Financial analysts quantify investment risk. Teachers analyze score distributions. Researchers report measurement precision. Our calculator serves all these use cases from one interface.