Standard Deviation Calculator
Calculate sample standard deviation, population standard deviation, variance, and data dispersion metrics.
8 numbers entered
Count (n)
8
Mean
5
Population Std Dev (σ)
2
Sample Std Dev (s)
2.13809
Population Variance (σ²)
4
Sample Variance (s²)
4.571429
Min
2
Max
9
Range
7
How to Use the Standard Deviation Calculator
- Enter a set of numbers separated by commas or spaces.
- The calculator computes sample size, arithmetic mean, and total variance.
- Review both Population (σ) and Sample (s) standard deviations.
Formulas & Principles
Mean: x̄ = (∑x_i) / n
Population Variance: σ² = ∑(x_i - μ)² / N
Sample Variance: s² = ∑(x_i - x̄)² / (n - 1)
Standard Deviation: σ = √(σ²), s = √(s²)
Frequently Asked Questions
What is the difference between sample (s) and population (σ) standard deviation?
Population standard deviation divides the sum of squared deviations by N. Sample standard deviation divides by n - 1 (Bessel's correction) to provide an unbiased estimate for sample data.
What does a high standard deviation indicate?
A high standard deviation indicates that data points are widely spread out over a broader range of values away from the mean.
What is variance in relation to standard deviation?
Variance is the average of squared differences from the mean; standard deviation is simply the square root of the variance.
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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