You enter a comma-separated list of numbers. The tool computes the mean (sum ÷ count), then finds how far each value deviates from the mean. It squares those deviations, sums them, and divides by n for the population variance or n − 1 for the sample variance. The standard deviation is the square root of the variance. It also reports count, sum, min, max, and range as summary statistics.
Use population (σ) when your data includes every member of the group you're studying — for example, test scores for an entire class. Use sample (s) when your data is a subset drawn from a larger group, which is the more common scenario in research and surveys.
It means your data points are widely spread from the mean. Whether a standard deviation is "large" depends on context — compare it to the mean. A coefficient of variation (std dev ÷ mean × 100) above 30% generally suggests high variability.
This is Bessel's correction. When you calculate the mean from a sample, you've already "used" one degree of freedom. Dividing by n − 1 compensates for this, producing an unbiased estimate of the population variance.
Yes — paste your values and they'll be parsed as long as they're separated by commas. If your spreadsheet copies values separated by tabs or newlines, add commas between them first.
With one data point, population standard deviation is 0 (no spread). Sample standard deviation is undefined because you'd divide by n − 1 = 0. You need at least two data points for a meaningful sample standard deviation.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.