What proportion of the data falls within one standard deviation of the mean according to the Empirical Rule?

The Empirical Rule, also known as the 68-95-99.7 rule, specifically states that in a normal distribution, about 68% of the data falls within one standard deviation of the mean. This is a fundamental concept in statistics that helps describe how data behaves in a perfectly symmetrical, bell-shaped distribution.

To understand this rule, consider a normal distribution curve where the mean is located at the center. The area under the curve represents the entirety of the data. When you look at one standard deviation on either side of the mean, you capture a significant portion of the data points—68% to be precise. This is crucial for various statistical analyses because it allows for the estimation of data tendencies and variability.

In contrast, the other values provided represent the percentages of data that fall within different ranges of standard deviations from the mean. For instance, 95% of the data falls within two standard deviations, and 99.7% falls within three standard deviations. Understanding these percentages helps in analyzing data distributions and making predictions based on statistical principles. Therefore, the proportion of data that falls within one standard deviation of the mean being 68% is a central element of interpreting normal distributions in statistics.