📐 Statistical Dispersion & Variance
Standard Deviation & Variance Calculator
Compute Sample Standard Deviation ($s$), Population Standard Deviation ($\sigma$), Sample Variance ($s^2$), Mean ($\bar{x}$), and Sum of Squared Deviations ($\Sigma (x_i - \bar{x})^2$).
Data Input
Sample Set A (n=8)
Uniform Set (n=6)
High Mean (n=5)
Sample Standard Deviation ($s$)
5.2372
Sample Mean ($\bar{x}$)
18.0000
Sample Variance ($s^2$)
27.4286
Count ($n$)
8
Sum of Values ($\Sigma x$)
144.00
Sum of Squares ($SS$)
192.00
💡 Step-by-Step Bessel's Correction:
$$s = \sqrt{\frac{\Sigma (x_i - \bar{x})^2}{n - 1}} = \sqrt{\frac{192.00}{7}} = 5.2372$$
Understanding Standard Deviation Formulas
Standard deviation measures the average distance of data points from the dataset's arithmetic mean:
- Sample Standard Deviation: $$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2}$$
- Population Standard Deviation: $$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}$$