What percentage of data lies within one standard deviation of the mean in a normal distribution?

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This property stems from the characteristics of the normal distribution, which is symmetric and bell-shaped. The empirical rule, also known as the 68-95-99.7 rule, states that:

• About 68% of the data points lie within one standard deviation (±1σ) from the mean.

• Approximately 95% fall within two standard deviations (±2σ).

• Roughly 99.7% are contained within three standard deviations (±3σ).

Understanding this concept is crucial in statistics and mass appraising, as it helps in assessing the spread and variability of data relative to the mean, which is vital for making informed judgments about property values and trends. The correct choice highlights a fundamental aspect of data distribution that plays a significant role in analysis and interpretation for various applications, including real estate appraisal and market analysis.