Approximately what percent of data in a normal distribution lies within one standard deviation of the mean?

• A. About 95%
• B. About 50%
• C. About 68%
• D. About 99.7%

Answer: (C)

In a normal distribution, the spread is measured by the standard deviation, and the curve is symmetric around the mean. About one standard deviation on either side of the mean captures the central portion of the data. Specifically, the area from -1 to +1 in z-scores covers roughly 0.6826 of the total area, which is about 68% of the data. This is part of the familiar 68-95-99.7 rule: roughly 16% lies beyond one standard deviation on each tail, so about 32% are outside and about 68% are inside. So the best answer is that about 68% of the data lie within one standard deviation of the mean.