How spread out is your data? Our variance calculator measures data dispersion by computing both population and sample variance β essential for statistics coursework, financial risk analysis, quality control, and scientific research.
What is Variance?
Variance measures how far data points are spread from the mean. A low variance means values cluster tightly around the average. A high variance means they are widely spread. Variance is the square of standard deviation and is used extensively in statistics, finance (portfolio risk), and machine learning.
Formula
Population Variance (ΟΒ²) = Ξ£(x β ΞΌ)Β² / N
Sample Variance (sΒ²) = Ξ£(x β xΜ)Β² / (Nβ1)
Where ΞΌ (or xΜ) = mean, N = count of data points
Example Calculation
Dataset: {2, 4, 6, 8, 10}
- Mean = (2+4+6+8+10)/5 = 6
- Deviations: (β4)Β², (β2)Β², 0Β², 2Β², 4Β² = 16, 4, 0, 4, 16
- Sum of squared deviations = 40
- Population Variance = 40/5 = 8
- Sample Variance = 40/4 = 10
How to Use This Calculator
- Enter numbers separated by commas.
- Click Calculate to see both population and sample variance, plus the mean.
Real Life Use Cases
- Finance: Measure the volatility/risk of a stock's daily returns over a period.
- Quality Control: Low variance in product dimensions = consistent manufacturing.
- Academics: Understand how spread student scores are around the class average.
- Climate Science: Measure temperature variation across months or years.
FAQs
When do I use population vs sample variance?
Use population variance when you have data for the entire group. Use sample variance when your data is a sample from a larger population β it uses Nβ1 for an unbiased estimate.
What is the relationship between variance and standard deviation?
Standard deviation (SD) = βVariance. SD is in the same units as the original data, making it more interpretable than variance (which is in squared units).
Common Use Cases for Variance Calculator
- Use this Variance Calculator for quick, accurate online calculations β no app needed
- Ideal for students, professionals, and anyone planning finances or health goals
- Get instant results right in your browser β 100% private, no data stored
- Bookmark this page to use the Variance Calculator anytime, on any device