In a normal distribution, what percentage of cases does one standard deviation encompass?

In a normal distribution, the empirical rule—also known as the 68-95-99.7 rule—states that approximately 68% of the data falls within one standard deviation (plus or minus) from the mean. This means that if you take a normally distributed dataset, and you were to calculate the mean and then identify the range that is one standard deviation above and below this mean, around 68% of the observations will lie within this range.

This characteristic of normal distribution is fundamental in statistics, as it helps in understanding the spread and likelihood of data points relative to the mean. Recognizing this property allows analysts to make predictions, conduct hypothesis testing, and assess probabilities effectively.

Understanding that each standard deviation from the mean represents a significant portion of the data is essential for interpreting statistical results and for applying various statistical methods accurately.