Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is from their average (mean). A low standard deviation means values cluster close to the mean; a high one means they are spread widely.

Population standard deviation (σ) is used when you have data for every member of the whole group and divides by n. Sample standard deviation (s) is used for a subset of the population and divides by (n − 1), which gives an unbiased estimate of the population standard deviation.

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance. Variance is in squared units (e.g., kg²), while standard deviation is in the same units as the original data (e.g., kg).

In finance, it measures the volatility of investment returns (e.g., naira exchange rate fluctuations). In education, it shows how evenly or unevenly students scored on an exam. In agriculture, it can measure variability in crop yields across different farms.

If all values are identical, the standard deviation is 0, meaning there is no variation in the dataset. This would be unusual in most real-world datasets.