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Empirical Rule (68-95-99.7)

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About This MicroSim

Visualize the Empirical Rule (also called the 68-95-99.7 Rule) for normal distributions.

How to Use

  • Click 1σ, 2σ, or 3σ buttons to see cumulative regions
  • Each click animates the region filling from the mean outward
  • Use ◀ ▶ arrows to switch between real-world examples (IQ, Heights, Test Scores)
  • Click Animate to see all three regions build sequentially
  • Click Clear to reset the view

Key Insights

  • 68% of data falls within ±1 standard deviation of the mean
  • 95% of data falls within ±2 standard deviations
  • 99.7% of data falls within ±3 standard deviations
  • Values beyond 3σ are extremely rare (<0.3%)

Lesson Plan

Learning Objective

Students will apply the 68-95-99.7 rule to estimate proportions and identify unusual values in normally distributed data (Bloom's Taxonomy: Applying, Evaluating).