📊 Standard Deviation Calculator
Calculate population and sample standard deviation, variance, mean, sum, and count from your data set.
Standard Deviation Calculator
This calculator computes comprehensive descriptive statistics for any data set. Enter your numbers separated by commas or new lines to instantly get the count, sum, mean, population variance, sample variance, population standard deviation, and sample standard deviation.
Standard deviation measures how spread out the numbers in a data set are. A low standard deviation means values tend to be close to the mean, while a high standard deviation means values are spread over a wider range. It is one of the most commonly used measures of statistical dispersion.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation (σ) divides by N and is used when your data represents an entire population. Sample standard deviation (s) divides by N-1 (Bessel's correction) and is used when your data is a sample from a larger population. Sample standard deviation gives an unbiased estimate of the population parameter.
What is variance?
Variance is the average of the squared differences from the mean. Standard deviation is the square root of variance. Variance measures the spread of data points, but its unit is squared, making standard deviation more interpretable since it uses the same units as the data.
When should I use population vs sample standard deviation?
Use population standard deviation when you have data for every member of the population (e.g., all students in a class). Use sample standard deviation when your data is a subset of a larger group (e.g., surveying 100 people from a city). If you are unsure, sample standard deviation is the safer choice as it provides a better estimate.