Standard Deviation Calculator

Enter your data points separated by commas, spaces, or new lines:

Statistical Results

Sample Size (n)

Mean (μ)

20.00

Sample Std Dev (s)

7.91

Population Std Dev (σ)

7.07

Variance (s²)

62.50

Sum

100

Minimum

Maximum

Data Points

Calculation Steps

1. Data points: 10, 15, 20, 25, 30

2. Mean (μ) = (10 + 15 + 20 + 25 + 30) ÷ 5 = 20

3. Sum of squared differences: (10-20)² + (15-20)² + (20-20)² + (25-20)² + (30-20)² = 250

4. Sample variance (s²) = 250 ÷ (5-1) = 62.5

5. Sample standard deviation (s) = √62.5 ≈ 7.91

6. Population variance (σ²) = 250 ÷ 5 = 50

7. Population standard deviation (σ) = √50 ≈ 7.07

Data Distribution

About Standard Deviation

What is Standard Deviation?

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates values are close to the mean, while a high standard deviation indicates values are spread out.

Sample vs Population

Use sample standard deviation when working with a subset of data, and population standard deviation when you have data for the entire population. The formulas differ by using n-1 for sample and n for population.

Applications

Standard deviation is used in finance for risk assessment, in quality control for process variation, in research for data analysis, and in many scientific fields to understand data distribution.

Interpretation

About 68% of values fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations (in a normal distribution).