According to the empirical rule, what percentage of data points fall within one standard deviation in a normally distributed population?

In a normally distributed population, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the data points will fall within one standard deviation of the mean. This rule is a fundamental concept in statistics, reflecting the properties of the normal distribution, which is symmetrical and bell-shaped.

Here’s how it works: if you plot the data on a graph, about 68% of the values will lie within the range defined by the mean minus one standard deviation and the mean plus one standard deviation. This provides useful insights into the variability of data and is commonly applied in fields such as psychology, finance, and the natural sciences, where the assumption of normality frequently applies.

The other percentages associated with the empirical rule—95% within two standard deviations and 99.7% within three standard deviations—are important as well, but they specifically address larger ranges beyond one standard deviation, which is why they pertain to higher percentages. Understanding that 68% of data falls within this first standard deviation is crucial for interpreting statistical data correctly.