What does standard deviation measure in a set of numbers?

Standard deviation measures how much the numbers in a set vary from the mean, providing insight into the spread or dispersion of the data points. A low standard deviation indicates that the numbers are close to the mean, suggesting that there is little variation among the values. Conversely, a high standard deviation means the numbers are spread out over a wider range and may be further from the mean. This measure is critical in understanding the consistency and variability of a dataset, particularly in educational assessments, where understanding student performance relative to the average is essential. By emphasizing how individual scores deviate from the average, standard deviation offers valuable information about performance variations among students, which can inform instructional adjustments and interventions.