Standard Deviation Calculator

Calculate standard deviation and variance

Browser ProcessingYour data never leaves your browser

Standard Deviation

5.2372

Variance

27.4286

Additional Statistics

Mean (μ):18.0000Count (n):8Sum of Squares:192.0000Coefficient of Variation:29.10%
Show Calculation Steps

1. Mean (μ) = Σx / n = 144 / 8 = 18.0000

2. Deviations from mean (x - μ):

10 - 18.0000 = -8.0000, 12 - 18.0000 = -6.0000, 23 - 18.0000 = 5.0000, 23 - 18.0000 = 5.0000, 16 - 18.0000 = -2.0000, 23 - 18.0000 = 5.0000, 21 - 18.0000 = 3.0000, 16 - 18.0000 = -2.0000

3. Squared deviations (x - μ)²:

64.0000, 36.0000, 25.0000, 25.0000, 4.0000, 25.0000, 9.0000, 4.0000

4. Sum of squared deviations = 192.0000

5. Variance (σ²) = 192.0000 / 7 = 27.4286

6. Standard Deviation (σ) = √27.4286 = 5.2372

Data Distribution (68-95-99.7 Rule)

Within 1σ (68%):12.76 to 23.24
Within 2σ (95%):7.53 to 28.47
Within 3σ (99.7%):2.29 to 33.71

Related Tools

Scientific CalculatorAdvanced scientific calculator with functions
Percentage CalculatorCalculate percentages, increases, and decreases
Fraction CalculatorAdd, subtract, multiply, divide fractions
Ratio CalculatorCalculate and simplify ratios