Standard Deviation Calculator
Calculate standard deviation and variance with detailed statistical analysis
Standard Deviation Calculator
Calculate the standard deviation and variance of a dataset. Our calculator supports both population and sample standard deviation calculations with detailed step-by-step results.
đĸ Data Input
đ Calculation Results
Frequency Table
đ Calculation Steps
đ Understanding Standard Deviation
What is Standard Deviation?
Standard deviation (Ī) measures how spread out data points are from the mean. A low standard deviation means data points are close to the mean, while high standard deviation indicates greater variability.
Population vs Sample
Use Population when you have all possible data points. Use Sample when your data represents a subset of a larger population and you want to estimate the population standard deviation.
Applications
Standard deviation is widely used in statistics, quality control, finance (risk assessment), weather analysis, and scientific research to understand data variability.
Population Standard Deviation
The population standard deviation is used when an entire population can be measured, and is the square root of the variance of a given data set. The formula is: Ī = â(ÎŖ(xi - Îŧ)² / N)
Where xi is an individual value, Îŧ is the mean/expected value, and N is the total number of values.
Sample Standard Deviation
When it's not possible to sample every member of a population, we use sample standard deviation. The formula uses N-1 in the denominator (Bessel's correction): s = â(ÎŖ(xi - xĖ)² / (N-1))
This correction reduces bias in the estimation of population standard deviation from sample data.