In a normal distribution, what percentage of scores typically falls within one standard deviation of the mean?

In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean. This is a fundamental property of the normal distribution, often referred to in statistics by the empirical rule or the 68-95-99.7 rule. This rule indicates that:

• About 68% of the data points lie within one standard deviation on either side of the mean.

• About 95% of the data points fall within two standard deviations of the mean.

• About 99.7% of the data points are found within three standard deviations of the mean.

Understanding this concept is crucial when analyzing data, as it provides insights into the distribution of scores and helps in determining how much of the data can be expected to fall within certain ranges. This knowledge is widely applied in various fields such as psychology, quality control, finance, and other areas that utilize statistical analysis.

The other percentages mentioned, such as 50%, 75%, and 95%, do not accurately represent the data falling within one standard deviation from the mean in a normal distribution. While 95% is associated with two standard deviations, the correct figure for one standard deviation remains firmly at 68%.