Variance

σ2=1ni=1n(xiμ)2\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \mu)^2

Description

Measures the spread of data from the mean.

Variables

Symbol Meaning
σ² Variance
n Number of values
xᵢ Individual values
μ Mean

Example

Problem

Find variance of 2,4,6,8,10 (mean=6)

Solution

σ² = [(16+4+0+4+16)/5] = 8

Real-World Applications

  • Data analysis
  • Quality control
  • Finance