Understanding Standard Deviation

A comprehensive guide to statistical dispersion measurement

What is Standard Deviation?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a dataset. It indicates how much the data points differ from the mean (average) value.

Low Standard Deviation

Data points are clustered closely around the mean

High Standard Deviation

Data points are spread out over a wider range

Population vs. Sample Standard Deviation

Population (σ)

  • Used when you have data for an entire population
  • Divides by N (total number of values)
  • Provides the true spread of the population

Sample (s)

  • Used when you have data from a sample of the population
  • Divides by (N-1) to account for sampling bias
  • Estimates the population standard deviation

Real-World Applications

Finance

Measuring investment risk and market volatility

Quality Control

Monitoring manufacturing processes and product consistency

Research

Analyzing experimental data and survey results

Education

Evaluating test scores and student performance

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