Standard Deviation

📊 intermediate

$$\sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{N}}$$

Quantifies the amount of variation or dispersion of a set of data values.

Variables & Units

$\sigma$

Population standard deviation

Unit: Same as data units

$x_i$

Individual data point

Unit: Unit of measurement

$\mu$

Population mean

Unit: Unit of measurement

$N$

Total number of observations

Unit: Dimensionless

Key Information

📐 Derived From

Square root of variance.

💡 Example

Determining the volatility of stock prices.

🔧 Applications

Quality control, finance, and social sciences.

⚠️ Constraints

Requires a normal distribution for some interpretations.

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