Variance Calculator
Variance - Solve mathematical problems with step-by-step solutions.
Variance Calculator
For Sample & Population Data
Variance
Variance measures how far a set of numbers is spread out from their average value. It is the average of the squared differences from the Mean. A high variance indicates that the numbers are very spread out; a low variance indicates they are clustered closely around the mean.
How the Variance Calculator Works
Variance measures how spread out a set of numbers is from their average (mean). It's calculated by finding the average of the squared differences from the mean. A low variance means data points are close together; a high variance means they're more spread out.
Key Formulas
- Population: σ² = Σ(x - μ)² / N
- Sample: s² = Σ(x - x̄)² / (n-1)
- Std Dev: σ = √(variance)
Calculating Variance
Step-by-Step Process
- Find the mean: Add all values and divide by the count
- Find deviations: Subtract the mean from each value
- Square deviations: Square each deviation to make them positive
- Average squared deviations: Divide by N (population) or n-1 (sample)
Example: Data Set [4, 8, 6, 5, 3]
- Step 1: Mean = (4+8+6+5+3) / 5 = 5.2
- Step 2: Deviations = [-1.2, 2.8, 0.8, -0.2, -2.2]
- Step 3: Squared = [1.44, 7.84, 0.64, 0.04, 4.84]
- Step 4: Sample variance = 14.8 / 4 = 3.7
Population vs Sample Variance
Population Variance (σ²)
Use when you have data for the entire population. Divide by N (total count).
Sample Variance (s²)
Use when you have a sample from a larger population. Divide by n-1 (Bessel's correction).
Real-World Applications
Quality Control
Manufacturing uses variance to ensure product consistency. Low variance means products are uniform.
Finance & Investing
Portfolio variance measures investment risk. Higher variance indicates more volatile returns.
Weather Forecasting
Variance helps quantify prediction uncertainty and temperature variability over time.
Sports Analytics
Variance measures player consistency. Low variance means reliable, predictable performance.
Frequently Asked Questions
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