Step-by-Step Process

1. Find the mean: Add all values and divide by the count
2. Find deviations: Subtract the mean from each value
3. Square deviations: Square each deviation to make them positive
4. 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 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).

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.