Approximately what range contains 68% of a population for a normally distributed trait?

Approximately what range contains 68% of a population for a normally distributed trait?

• A. Mean plus or minus 2 standard deviations
• B. Mean plus or minus 1 standard deviation
• C. Median plus or minus 1 standard deviation
• D. Mean plus or minus 3 standard deviations

Answer: (B)

In a normal distribution, the spread around the center is measured by the standard deviation, and about 68% of values fall within one standard deviation of the mean. So the range from mean minus one standard deviation to mean plus one standard deviation contains roughly 68% of the population. This is part of the 68-95-99.7 rule: about 95% lie within two standard deviations, and about 99.7% within three. The idea is that the mean is the center of a symmetric distribution, so one standard deviation around that center captures the majority of observations.

In a normal distribution, the spread around the center is measured by the standard deviation, and about 68% of values fall within one standard deviation of the mean. So the range from mean minus one standard deviation to mean plus one standard deviation contains roughly 68% of the population. This is part of the 68-95-99.7 rule: about 95% lie within two standard deviations, and about 99.7% within three. The idea is that the mean is the center of a symmetric distribution, so one standard deviation around that center captures the majority of observations.