Please provide numbers separated by commas to calculate the standard deviation, variance, mean, sum, and margin of error.
Standard deviation measures how spread out a set of numbers is from their average — a low value means the numbers cluster tightly around the mean, a high value means they're widely scattered. This calculator supports both population and sample standard deviation, which use slightly different formulas depending on whether your data represents an entire population or just a sample of it.
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.
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 when you have data for the entire group. Use sample standard deviation for a subset of data, which 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 to get the 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.
Yes, it calculates mean, variance, and standard deviation for any data set, with a full breakdown of each step.