According to standard deviation, what percentage of the population falls within 1 SD of the mean?

The correct answer, indicating that approximately 68% of the population falls within one standard deviation of the mean, is rooted in the properties of a normal distribution. In a normal distribution, the data is symmetrically distributed around the mean, and the standard deviation serves as a measure of variability or dispersion.

In statistical terms, if we consider a bell-shaped curve representing the normal distribution, one standard deviation above and below the mean encompasses a specific range of scores. According to the empirical rule (also known as the 68-95-99.7 rule), about 68% of the data points will fall within one standard deviation from the mean. This rule is foundational in statistics and illustrates how data clusters around the mean, allowing for predictions about the population based on the mean and standard deviation.

This understanding is essential for school counselors when interpreting data related to student performance, behavior, and other variables, as it can help in identifying how individual students compare to their peers.