✓ Mathematical
◆ The Patternσ = √(Σ(x−μ)²/N).
Standard Deviation — the statistical building block of volatility measurement.
σ = √(Σ(x − μ)² / N)
where μ = mean, N = number of observations
where μ = mean, N = number of observations
Higher σ = more volatility = prices are spread far from the mean.
In markets:
• Historical Volatility = σ of returns × √252 (annualized)
• 1σ covers ~68% of observations
• 2σ covers ~95% → basis of Bollinger Bands
• 3σ events are "rare" but happen more often in markets than normal distributions predict (fat tails)
• Historical Volatility = σ of returns × √252 (annualized)
• 1σ covers ~68% of observations
• 2σ covers ~95% → basis of Bollinger Bands
• 3σ events are "rare" but happen more often in markets than normal distributions predict (fat tails)
Pattern bridge: This is standard deviation from statistics, applied to price returns. In ML, it’s the denominator in batch normalization and the width of Gaussian distributions.