Empirical Rule (68–95–99.7)
Share of data within 1, 2, 3 standard deviations.
Key idea
Share of data within 1, 2, 3 standard deviations.
In depth
For a normal distribution, about 68% of values lie within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. A quick way to judge how unusual a value is.
Worked example
Test scores μ = 70, σ = 10: 95% fall in 50 to 90.
Real-world uses
- Quickly estimating how many students score within two standard deviations of the mean
Common mistake
Using it for skewed or non-normal data.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Empirical Rule (68–95–99.7)?
Share of data within 1, 2, 3 standard deviations. It is a topic at the advanced level in Probability & Statistics.
Where is Empirical Rule (68–95–99.7) used in real life?
Real-world examples: Quickly estimating how many students score within two standard deviations of the mean.
What should I learn before Empirical Rule (68–95–99.7)?
Make sure you are comfortable with Normal Distribution, the previous topic in Probability & Statistics.
What is a common mistake with Empirical Rule (68–95–99.7)?
Using it for skewed or non-normal data.
How can I practise Empirical Rule (68–95–99.7)?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Empirical Rule (68–95–99.7)?
Move on to Standard Normal and z-Tables next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.