Free Mean, Variance, and Standard Deviation Calculator
Enter your values below (comma, space, or new line separated), choose sample or population mode, and click calculate.
What this calculator does
This statistics calculator gives you the three core measures people search for most often: mean (average), variance, and standard deviation. It also reports useful helpers like count, sum, minimum, maximum, range, and median, so you can quickly understand your dataset without moving to a spreadsheet.
Whether you're working on homework, analyzing business metrics, checking lab measurements, or reviewing test scores, this tool saves time and reduces manual calculation errors.
Quick definitions
Mean
The mean is the average value of a dataset. Add all values and divide by the number of values.
Formula: mean = (x1 + x2 + ... + xn) / n
Variance
Variance measures spread. It tells you how far values are from the mean, on average (in squared units).
- Population variance: divide by n
- Sample variance: divide by n - 1 (Bessel's correction)
Standard deviation
Standard deviation is the square root of variance. It gives spread in the same units as your original data, making interpretation easier.
Population vs. sample: which should you choose?
Use population when your dataset includes every value in the group you care about. Use sample when your dataset is only part of a larger group and you want to estimate full-population spread.
- All 30 students in one class measured? Usually population.
- 30 customers sampled from 20,000 total customers? Sample.
How to use the calculator
- Paste or type your numbers in the data field.
- Select Population or Sample.
- Set decimal precision (optional).
- Click Calculate to see results instantly.
If you just want to test the tool, click Load Example.
Worked example
Suppose your values are: 10, 12, 15, 18, 20.
- Mean = 15
- Population variance = 14.8
- Population standard deviation = 3.8471
If treated as a sample instead, variance and standard deviation are slightly larger because the formula divides by n - 1.
Why these metrics matter
In finance
Mean returns show typical performance, while standard deviation helps estimate volatility (risk).
In education
Average score tells class performance; standard deviation reveals whether students cluster tightly or vary widely.
In quality control
Low standard deviation often means a stable process. High deviation can indicate inconsistency that needs investigation.
Common mistakes to avoid
- Using sample variance when you really have full population data (or vice versa).
- Mixing units (for example, centimeters and meters in one list).
- Forgetting that variance is in squared units, while standard deviation is in original units.
- Relying only on mean when the dataset has strong outliers.
Related tools and search terms
People often find this page while looking for an average calculator, statistics calculator, standard deviation formula, sample variance calculator, population variance calculator, and descriptive statistics calculator. This tool is designed to cover all those needs in one place.
FAQ
Can I enter decimals and negative numbers?
Yes. Values like -3.5, 0, 7.25, and 100 are all valid.
What separators can I use?
Commas, spaces, semicolons, and line breaks are all accepted.
Do I need at least two values?
For sample variance and sample standard deviation, yes. Population calculations can be done with one value.