Variance measures how spread out a set of numbers is. It is the average of the squared differences from the mean. For the numbers 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5. The squared differences are 9, 1, 1, 1, 0, 0, 4, 16. Their average is 4, so the variance is 4.

Squaring makes all differences positive and gives more weight to large deviations. The square root of the variance is the standard deviation. Variance is denoted σ² for a population and s² for a sample.

Variance appears in statistics, finance, and quality control. In finance, it measures the volatility of returns. In quality control, it tracks consistency. The concept is central to understanding spread and uncertainty in data.

• Average of squared differences from the mean
• Square root is standard deviation
• Denoted σ² or s²
• Measures spread and volatility