Variance and Standard Deviation Calculator
Calculate population or sample variance, standard deviation, mean, and count from a numeric data set.
Calculate Variance and Standard Deviation
Calculate population or sample variance, standard deviation, mean, and count from a numeric data set.
What This Variance and Standard Deviation Calculator Calculates
Variance measures how far values are spread around their arithmetic mean, while standard deviation expresses that spread in the original unit of measurement. This calculator supports both population and sample formulas. The distinction matters because sample variance divides by n−1 rather than n to estimate population variability from a sample. The calculation is completed locally in the browser, and the calculator itself does not require an account or send the entered values to OfficeCalculator.Net for server-side calculation.
Formula and Method
Population variance = Σ(x − mean)² ÷ n; sample variance = Σ(x − mean)² ÷ (n − 1).
The result is calculated from the values currently shown in the form. Supporting figures are included so you can inspect the intermediate meaning of the answer rather than relying on an unexplained single number.
How to Use the Calculator
- Enter the requested date, time, score, data values, or planning assumptions using the labels shown beside each field.
- Keep related inputs on the same basis. For example, pair values with their matching weights and use the weekend or time-zone convention that actually applies.
- Select Calculate and review both the main result and the supporting figures.
- Read the interpretation and limitations below before using the result in a real workflow.
- Use Copy Result, Share Result, or Save Result Image when you need a record of the calculation.
Worked Example
Enter a small set such as 10, 12, 13, 15, and 20. The calculator first finds the mean, measures each value's squared deviation from that mean, sums those squared deviations, and then divides by n for population variance or n−1 for sample variance.
Common Uses
- Describe variability in measurements, scores, process data, or financial observations.
- Check manual statistics homework or spreadsheet calculations.
- Compare sample and population standard deviations for the same data.
How to Interpret the Result
Variance is expressed in squared units, so standard deviation is often easier to interpret directly. A value of zero means every observation is identical. Larger values indicate greater dispersion, but whether a standard deviation is considered large depends on the scale and context of the data.
For repeat calculations, change one assumption at a time and compare the supporting figures. That makes it easier to identify which input is driving the result and reduces the chance of carrying an incorrect unit, date convention, or percentage basis into a decision.
Important Notes and Limitations
Variance and standard deviation can be strongly affected by outliers and do not by themselves establish whether data are normally distributed. Choosing sample versus population variance should reflect how the data are being used. Statistical inference may require additional assumptions, sampling design, confidence intervals, or robust measures of spread.
OfficeCalculator.Net provides this tool for planning, checking, learning, and general informational use. Keep source records and official system outputs when a result affects grades, payroll, contractual service levels, formal reports, or another decision that must be verified independently.
Frequently Asked Questions
When should I choose sample variance?
Choose sample variance when the entered observations are a sample used to estimate variability in a larger population.
Why is sample variance usually larger?
It divides the sum of squared deviations by n−1 instead of n, applying Bessel’s correction.
What unit is standard deviation in?
Standard deviation uses the same unit as the original data, while variance uses squared units.
Common Search Questions About Variance and Standard Deviation Calculator
How do I calculate variance and standard deviation?
Use the calculator on this page and enter the requested values. Calculate population or sample variance, standard deviation, mean, and count from a numeric data set.
How can I get the variance and standard deviation result quickly?
Enter the required values, calculate, and review the result together with its supporting figures. On rebuilt mobile calculators, the answer is brought into the current viewport so the result is easy to find.
What values do I need to calculate variance and standard deviation?
Use the inputs shown in the calculator form and keep units consistent. For important decisions, use measured or verified values and review the page assumptions before relying on the result.