Average & Standard Deviation Calculator
Last updated: 2026-06-25
The arithmetic mean is sum ÷ count, the variance is the mean of the squared deviations, and the standard deviation is the square root of the variance. Sample standard deviation divides by n−1 instead of n (Bessel's correction).
Enter your numbers below to get the count, sum, mean, median, variance and standard deviation at once.
Data set statistics
Mean (arithmetic average)
0
| Item | Value |
|---|---|
| Count (n) | |
| Sum | |
| Mean | |
| Median | |
| Minimum | |
| Maximum | |
| Variance | |
| Standard deviation |
Results are rounded to 6 decimal places. Sample standard deviation is only computed when there are at least two values.
How to use
- Enter data — Enter the numbers separated by commas, spaces or line breaks.
- Choose the standard deviation basis — Select sample standard deviation (n−1) or population standard deviation (n).
- View the result — Press Calculate to see count, sum, mean, median, minimum, maximum, variance and standard deviation in a table.
How to calculate mean, median and standard deviation
The mean and median describe a typical value, while the variance and standard deviation describe spread; together they are the most basic summary statistics. The mean reflects every value evenly but is sensitive to outliers, whereas the median is the middle value in order and is robust to outliers.
| Statistic | Formula |
|---|---|
| Mean | (x₁ + x₂ + … + xₙ) ÷ n |
| Median | Middle value after sorting (average of the two middle values if n is even) |
| Variance (population) | Σ(xᵢ − mean)² ÷ n |
| Variance (sample) | Σ(xᵢ − mean)² ÷ (n − 1) |
| Standard deviation | √variance |
Sample standard deviation applies Bessel's correction, dividing by n−1 to avoid underestimating spread when estimating a population from a sample. It is widely used for analyzing variation in real life — exam score distributions, measurement error, investment volatility. To compare changes as ratios, try the percentage calculator as well.
Frequently Asked Questions (FAQ)
How do I calculate the mean (arithmetic average)?
The arithmetic mean is the sum of all values divided by the number of values: mean = (x1 + x2 + … + xn) ÷ n.
How are the mean and median different?
The mean is the sum divided by the count, while the median is the middle value when the data is sorted. The mean is sensitive to extreme values (outliers), but the median is much less affected.
What is the difference between sample and population standard deviation?
Population standard deviation is the square root of the variance, dividing the sum of squared deviations by n. Sample standard deviation divides by n−1 (Bessel's correction). Use population for the entire data set, and sample when estimating a population from a sample.
What does standard deviation mean?
Standard deviation measures how spread out values are from the mean. A smaller value means the data is clustered near the mean; a larger value means it is more dispersed. It is the positive square root of the variance.
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Last updated: 2026-06-25