What does the 68-95-99.7 rule describe?

The 68-95-99.7 rule, also known as the empirical rule, describes how data is distributed in a normal distribution, which is a symmetrical, bell-shaped curve that represents the distribution of many types of data. According to this rule, approximately 68% of the data points lie within one standard deviation of the mean, about 95% of the data points lie within two standard deviations, and roughly 99.7% lie within three standard deviations. This provides a useful framework for understanding how data is spread around the mean in a normal distribution, indicating the concentration of data points close to the average value and how they taper off further from it.

This rule is foundational in statistics because it helps in making predictions about data and assessing probabilities, particularly in fields that rely on normal distributions, such as social sciences, natural sciences, and various industries. Understanding this concept is crucial for interpreting statistical data effectively and for conducting analyses that assume normality in datasets.