Standard Deviation Calculator
Paste a list — get mean, variance, and SD. Click any i for detail.
Data
Numbers
i
List
Comma or space separated. |
|
|---|---|
Type
i
SD
Sample uses n−1; population uses n. |
How to use this calculator
- Paste numbers separated by commas or spaces.
- Choose sample (n−1) or population (n) deviation.
- Read mean, variance, and standard deviation.
- Use sample SD when your list is a sample from a larger group.
Results explained
Standard deviation measures spread around the mean. Sample mode divides by n−1 to correct for estimating the mean from the same data. Population mode divides by n.
Quick reference: SD
Sample SD uses n−1 in the denominator; population SD uses n.
| Item | Detail |
|---|---|
| Variance | SD squared |
| Sample | n−1 denominator (typical for lab samples) |
| Population | n denominator (whole group known) |
| Minimum data | Need at least 2 numbers for sample SD |
Mean/median/mode is a different page; z-scores need a known μ and σ.
How the estimate is built
μ = Σx/n; variance = Σ(x−μ)² / (n or n−1); SD = √variance.
Example scenario
2, 4, 4, 4, 5, 5, 7, 9 → sample SD about 2.14.
FAQ
When should I pick sample vs population?
Sample when your list is a subset you want to generalize from. Population when you truly have every member.
Why is my SD zero?
All numbers are identical, so spread is zero.
Does this compute z-scores?
No. You need a separate mean and SD reference for z = (x−μ)/σ.