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

Question

Accepted Answer

68%. In a normal (bell-shaped) distribution, approximately 68% of all data values fall within one standard deviation of the mean (between μ - σ and μ + σ). This is part of the empirical rule (68-95-99.7 rule), which describes the distribution of data in any normal distribution.

50% of data falls below (or above) the mean in a symmetric distribution, but this represents only the split at the center, not the spread within one standard deviation. 95% of data falls within two standard deviations of the mean (between μ - 2σ and μ + 2σ), not one standard deviation. 99.7% of data falls within three standard deviations of the mean (between μ - 3σ and μ + 3σ), which encompasses nearly all observations.

The empirical rule (68-95-99.7 rule) for normal distributions is a key statistical concept on the DSST Business Mathematics exam. Students should memorize these three percentages and understand how to apply them to business problems, such as quality control limits, investment risk analysis, and sales forecasting where data follows an approximately normal distribution.

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