Please provide numbers separated by commas to calculate the standard deviation, variance, mean, sum, and margin of error.
Standard deviation measures how spread out values are around the mean. A small value means data clusters closely; a large value means data is widely spread. It is one of the most important measures in statistics, finance, and research.
Use population standard deviation (σ) when you have data for the entire group. Use sample standard deviation (s) for a subset of data — it uses n−1 in the denominator (Bessel's correction) to account for sampling uncertainty.
Calculate the mean, subtract it from each value and square the result, average those squared differences (variance), then take the square root. This calculator performs all steps and shows intermediate values.
In a normal distribution: 68% of values fall within 1 standard deviation, 95% within 2, and 99.7% within 3. This empirical rule is widely used to understand data distribution and identify outliers.