Standard deviation calculator
Compute population or sample standard deviation from up to 12 values while ignoring blank fields.
What this calculator covers
Use this calculator to measure how tightly values cluster around their mean, with a clear choice between population and sample formulas.
The walkthrough keeps the variance visible as a supporting step so the square-root relationship behind standard deviation never disappears.
Frequently asked questions
- When should I use population mode versus sample mode?
- Use population mode when your values represent every item in the group you care about. Use sample mode when your values are a subset drawn from a larger population — sample mode divides by n − 1 instead of n, which corrects for the tendency of a sample to underestimate the true spread.
- Why is standard deviation reported in the same units as the data while variance is not?
- Variance averages squared distances from the mean, so its unit is the square of whatever the data is measured in. Taking the square root returns the result to the original unit, which makes standard deviation easier to interpret alongside the data values.
- What does a standard deviation close to zero indicate?
- It means the values are tightly clustered around the mean with very little spread. A standard deviation of exactly zero would require all values to be identical.
- How many values does this calculator require?
- At least two filled numeric fields are needed because standard deviation requires more than one data point to measure any spread. Blank fields are ignored in the calculation.
Tool
Run the calculation
Result
RESULT · STANDARD DEVIATION
â„–156
Primary result
4.84768
Using the sample formula on 8, 12, 12, 15, 19, 21, the variance is 23.5 and the standard deviation is 4.84768.
- Values used
- 8, 12, 12, 15, 19, 21
- Mean
- 14.5
- sample variance
- 23.5
- sample standard deviation
- 4.84768
Step-by-step solution
- 1.Average the 6 values to get the mean 14.5.
- 2.Square each distance from the mean and divide by n - 1 to get the sample variance 23.5.
- 3.Take the square root of the variance to report the standard deviation 4.84768.
Walkthrough
Visual walkthrough
Standard deviation is the square root of variance, so the work moves from center to squared spread and back into the original units.
01
Anchor the data at the mean
Mean = 14.5
Deviation work starts by finding the balancing point of the entered values.
02
Compute the variance
sample divisor n - 1 → 23.5
Variance averages the squared distances from the mean using either n or n - 1 depending on the selected mode.
03
Take the square root
Square rooting the variance converts the spread back into the original data units.
4.84768 standard deviation