How is Standard Deviation related to distribution of scores?

Standard deviation is a statistical measurement that quantifies the amount of variation or dispersion of a set of scores relative to the mean (average) score. When considering distribution, standard deviation helps to understand how closely the scores cluster around the mean. A smaller standard deviation indicates that the scores are closely grouped around the mean, while a larger standard deviation shows that the scores are spread out over a wider range of values.

In the context of a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, and about 95% of the scores fall within two standard deviations. This property makes standard deviation a crucial component for interpreting the spread of scores in various contexts, such as academic assessments, psychological testing, and other research endeavors.

This understanding is fundamental in fields like counseling, where the interpretation of test scores can inform interventions and support decisions. For instance, if most scores fall within a narrow band around the mean, it suggests a more homogenous group, whereas a wide spread might indicate varying levels of need or different abilities among the individuals assessed.