According to the empirical rule, what percentage of data falls within one standard deviation of the mean?

The empirical rule, also known as the 68-95-99.7 rule, applies to normally distributed data. It states that approximately 68% of the data points will fall within one standard deviation from the mean. This means that if you were to visualize a normal distribution curve, you would find that when you measure one standard deviation above and below the mean, about 68% of the observations or data points would lie within that range.

This concept is crucial in statistics as it helps to understand the distribution of data and how concentrated the values are around the mean in a bell-shaped curve. Recognizing that 68% of data fall within this range allows statisticians and researchers to make predictions and understand variability in datasets effectively.

In contrast, the other percentages listed in the choices correspond to wider ranges within the normal distribution: about 95% of the data falls within two standard deviations from the mean, and around 99.7% falls within three standard deviations. Thus, identifying that the correct percentage for one standard deviation is 68% is essential in correctly applying the empirical rule to analyze datasets.