What percentage of data falls within 2 standard deviations in a normal distribution?

In a normal distribution, the empirical rule, also known as the 68-95-99.7 rule, provides a way to understand the distribution of data in relation to standard deviations from the mean. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, about 95% of the data is found within two standard deviations, and roughly 99.7% lies within three standard deviations.

When examining the distribution of data, understanding where the bulk of values lie helps in interpreting results, especially in fields requiring statistical analysis such as medical imaging. The range within two standard deviations is important because it captures the majority of variability in a normal dataset, which is useful when evaluating patient data in positron emission tomography (PET) scans or any other quantitative analysis.

This ability to quantify how much data falls within a specific range is crucial for determining normal versus abnormal results, making it essential for practitioners in the field. Thus, the statement that 95% of data falls within two standard deviations accurately reflects the empirical characteristics of a normal distribution.