Standard Deviation Calculator
Calculate standard deviation, variance, mean, and other key statistics for any data set. Choose between sample and population standard deviation with our free online calculator.
How to Use This Calculator
- Enter your data values separated by commas or spaces (e.g., 12, 15, 18, 21).
- Choose between Sample or Population standard deviation.
- Click Calculate Standard Deviation to view results.
- Review the mean, standard deviation, variance, quartiles, and sorted data list.
Formulas
σ = √(Σ(x − μ)² / N)
Sample Standard Deviation (s):
s = √(Σ(x − x̄)² / (n − 1))
Variance: σ² or s² = Sum of squared deviations / divisor
Mean (μ): Σx / n
IQR: Q3 − Q1
CV: (σ / μ) × 100%
Use population standard deviation when your data includes every member of the group. Use sample standard deviation when your data is a subset of a larger population.
Examples
Exam Scores
85, 90, 78, 92, 88, 95, 82, 91 — Mean = 87.63, Population σ = 4.89, Sample s = 5.24.
Daily Temperatures (°C)
22, 25, 28, 24, 30, 27, 26, 23, 29, 21 — Mean = 25.5, Population σ = 2.98.
Product Weights (g)
100, 102, 98, 101, 99, 103, 97, 100 — Mean = 100.0, Population σ = 2.0.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides by N (total count) and describes the entire dataset. Sample standard deviation (s) divides by n−1 (Bessel's correction) and estimates the standard deviation of a larger population from which the sample was drawn. Use sample when your data is a subset; use population when you have every data point.
What does standard deviation tell us?
Standard deviation measures how spread out the data values are from the mean. A low standard deviation indicates data points are clustered closely around the mean, while a high standard deviation indicates the data is widely spread out.
When should I use sample vs. population standard deviation?
Use population standard deviation when your data includes every member of the group (e.g., all students in a class). Use sample standard deviation when your data is a subset of a larger group (e.g., a survey of 100 people from a city of 1 million).
What is a good standard deviation?
There is no universally "good" standard deviation—it depends on context. A small standard deviation relative to the mean (low coefficient of variation) means data is consistent. In quality control, a smaller σ is better. In finance, a higher σ means more risk/volatility.