Empirical Rule
Also known as: 68-95-99.7 rule, three-sigma rule
Grade 9-12
In a normal distribution: ~68% of data falls within 1σ, ~95% within 2σ, and ~99. Quick way to understand spread in normal distributions; basis for z-scores and probability estimates.
Definition
In a normal distribution: ~68% of data falls within 1σ, ~95% within 2σ, and ~99.7% within 3σ of the mean.
💡 Intuition
Most data clusters near the center of a bell curve; the further from the mean, the rarer the value.
🎯 Core Idea
The empirical rule only applies to approximately normal distributions — not all data sets.
Example
Formula
🌟 Why It Matters
Quick way to understand spread in normal distributions; basis for z-scores and probability estimates.
Related Concepts
🚧 Common Stuck Point
The empirical rule does not apply to skewed or non-normal distributions.
Frequently Asked Questions
What is Empirical Rule in Statistics?
In a normal distribution: ~68% of data falls within 1σ, ~95% within 2σ, and ~99.7% within 3σ of the mean.
Why is Empirical Rule important?
Quick way to understand spread in normal distributions; basis for z-scores and probability estimates.
What do students usually get wrong about Empirical Rule?
The empirical rule does not apply to skewed or non-normal distributions.
What should I learn before Empirical Rule?
Before studying Empirical Rule, you should understand: stat normal distribution.
Prerequisites
How Empirical Rule Connects to Other Ideas
To understand empirical rule, you should first be comfortable with stat normal distribution.