In a normally distributed population, what percent of the data points will fall within one standard deviation?

In a normally distributed population, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68.3% of the data points will fall within one standard deviation of the mean. This guideline helps in understanding how data is spread out in a normal distribution.

The mean is the central point around which the data is distributed, and the standard deviation measures the dispersion of the data points from the mean. When you consider one standard deviation above and below the mean, you account for those data points that are closest to the average. This captures a significant proportion of the data, which is why 68.3% is the figure associated with this range.

In contrast, other percentages are associated with different ranges in the empirical rule; for example, around 95% of the data falls within two standard deviations from the mean, and about 99.7% falls within three standard deviations. Understanding this distribution is fundamental in a variety of fields, including statistics, science, and environmental studies, as it helps analysts evaluate variability and predict outcomes based on normal distribution patterns.