Calculate population and sample standard deviation, variance, mean, and sum of a dataset. Analyze data spread, standard error, and variance easily.
Standard deviation measures the amount of variation or dispersion in a set of data values. Our free online Standard Deviation Calculator calculates both population standard deviation (σ) and sample standard deviation (s) from your data, along with mean, variance, count, and sum.
The formula for sample standard deviation is s = √(∑(x_i - x_mean)^2 / (n - 1)), while the population standard deviation uses n in the denominator instead of n - 1. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates dispersion.
Population standard deviation is used when you have the complete dataset of the entire group. Sample standard deviation is used when the data is a representative subset of a larger population, using n-1 in the denominator to correct for bias.
A high standard deviation means that the data points are spread out over a wider range of values, indicating greater variability and less consistency in the dataset.
Standard deviation is the square root of variance. Variance measures the average squared deviations from the mean, while standard deviation brings the measurement back to the same unit as the original data.
In finance, standard deviation is widely used to measure risk and volatility. A higher standard deviation of investment returns indicates higher volatility and greater risk.