Variance Calculator
Calculate the variance of a data set
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Variable Mechanics
Roles, constraints & impacts
Numbers (comma-separated)
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Common Mistakes & Traps
- Confusing Population Standard Deviation (divide by N) with Sample Standard Deviation (divide by n - 1 for Bessel correction).
- Assuming all distributions are normal (skewed distributions make the median more reliable than mean).
- Outliers disproportionately distort the mean and variance.
Dimensional Analysis & Units
Mean & SD share the same unit as original data; Variance is in [Unit]².
Real-World & Industry Application
Quality control tolerances in manufacturing, stock market volatility metrics, clinical medical trials, and academic grading curves.
Worked Example: Variance
Given:
- numbers = 2, 4, 4, 4, 5, 5, 7, 9
- Data set: 2, 4, 4, 4, 5, 5, 7, 9
- Mean = 5
- Σ(x - μ)² = 32
- Variance = 32 ÷ 8 = 4
Answer: 4
Frequently Asked Questions
What is the Variance formula?
σ² = Σ(x - μ)² ÷ n. Calculate the variance of a data set.
How do I calculate Variance?
Enter Numbers (comma-separated) (numbers) into the calculator. It applies σ² = Σ(x - μ)² ÷ n and shows every step of the working.
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