What percentage of data is typically found within one standard deviation of the mean in a normal distribution?

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This is a fundamental property of normal distributions, often referred to in statistics as part of the empirical rule or the 68-95-99.7 rule.

This means that if you were to plot data that follows a normal distribution, about two-thirds of the data points would land within the range defined by the mean minus one standard deviation and the mean plus one standard deviation. This characteristic is significant in various statistical applications, including hypothesis testing and confidence intervals, as it helps in understanding how data is spread out around the mean.

Understanding this concept is crucial for interpreting data that follows a normal distribution and provides a foundation for more advanced statistical analysis. This concept is widely applied in fields like psychology, medicine, and social sciences, where normal distribution is often assumed for various types of data.