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Standard Deviation

σ=1n∑i=1n(xi−μ)2\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \mu)^2}

Description

Measures the amount of variation in a dataset.

Variables

Symbol Meaning
σ Standard deviation
n Number of values
xᵢ Individual values
μ Mean

Examples

Basic Calculation

Problem: Find std dev of 2,4,6,8,10

Solution:

σ = √8 ≈ 2.83

Real-World Applications

  • Data analysis
  • Quality control
  • Research