Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any dataset. Supports both population (σ) and sample (s) statistics with full breakdown.
10 values detected
Std Dev (s)
4.4672
Variance (s²)
19.9556
Mean (x̄)
7.2
Count (n)
10
Median
6.5
Min
1
Max
14
Range
13
What Is Standard Deviation?
Standard deviation measures how spread out the values in a dataset are from the mean (average). A low standard deviation means most values cluster close to the mean; a high standard deviation means values are spread widely. It is one of the most important statistics in data analysis, finance, science, and quality control.
Population vs Sample
- Population (σ): use when your dataset contains all members of the group. Variance divides by N.
- Sample (s): use when your dataset is a subset drawn from a larger population. Variance divides by N−1 (Bessel's correction) to get an unbiased estimate.
How to Use
- Enter numbers separated by commas, spaces, or new lines
- Toggle between Population and Sample mode
- Results show mean, variance, std dev, median, min/max, range, and mode
- The deviation table shows each value's distance from the mean
FAQ
What is variance?
Variance is the average of the squared differences from the mean. Standard deviation is its square root. Variance is expressed in squared units (e.g., cm²), while standard deviation is in the original units (e.g., cm), making it easier to interpret.
Why does sample standard deviation divide by N−1?
Dividing by N tends to underestimate the true population variance when working with a sample. Dividing by N−1 (Bessel's correction) corrects for this bias, giving a more accurate estimate of the population variance from sample data.
What does a standard deviation of 0 mean?
A standard deviation of 0 means all values in the dataset are identical — there is no spread at all. Every value equals the mean.
What is the empirical rule (68-95-99.7)?
For a normal distribution: ~68% of values fall within 1 standard deviation of the mean, ~95% within 2, and ~99.7% within 3. This is also called the three-sigma rule and is widely used in quality control and statistics.