Standard Deviation Calculator

Standard deviation measures how spread out values are from the mean. A low standard deviation means values cluster closely around the mean; a high standard deviation means they are spread over a wider range.

Use population standard deviation (σ) when your data represents the entire population. Use sample standard deviation (s) when your data is a sample from a larger population — it uses n-1 (Bessel's correction) to reduce bias.

Variance is the average of the squared differences from the mean. It measures how far the data is spread. Standard deviation is the square root of variance, expressed in the same units as the data.

The mean is the arithmetic average; it is affected by outliers. The median is the middle value when data is sorted; it is more robust to outliers. For skewed distributions, the median is often a better measure of central tendency.

The mode is the value that appears most frequently in the data set. There can be multiple modes (bimodal, multimodal) or no mode if all values appear the same number of times.