Standard Deviation Calculator
Calculate the standard deviation and variance of a data set.
Separate values with commas or spaces
Sample standard deviation
σ = 5.2372
Variance
0,0000
Mean
0,00
Range
0,00
Coefficient of variation
0,00 %
Data distribution
μ = 18.0
1023
Deviations table
| x | x - μ | (x - μ)² |
|---|---|---|
| 10 | -8.00 | 64.00 |
| 12 | -6.00 | 36.00 |
| 23 | 5.00 | 25.00 |
| 23 | 5.00 | 25.00 |
| 16 | -2.00 | 4.00 |
| 23 | 5.00 | 25.00 |
| 21 | 3.00 | 9.00 |
| 16 | -2.00 | 4.00 |
| Σ | - | 192.00 |
Formula
σ = √[ Σ(xᵢ - μ)² / (n-1) ]
Bessel's correction (n-1) for samples
What is standard deviation?
Standard deviation measures how much data is dispersed from the mean. A low value indicates data grouped close to the mean; a high value indicates greater dispersion.
Interpretation
In a normal distribution, approximately 68% of data is within ±1 standard deviation of the mean, 95% within ±2 deviations, and 99.7% within ±3 deviations (empirical rule).
Sample vs Population
Use population deviation when you have ALL the data. Use sample when analyzing a subset. Sample uses n-1 in the denominator to correct for bias.