25 students test grades (possible scores 0 to 100)has a standard deviation of 15. What logically follows???
The standard deviation measures the amount of variability or dispersion in a set of data. In this case, the standard deviation of 15 indicates that the data points, which represent the test grades of 25 students, are spread out around the mean grade.
Based on this information, it is logical to deduce that there is a considerable amount of variability or scatter in the test scores. This suggests that the students' performances on the test varied significantly, with some students achieving high scores and others scoring lower.
However, it is important to note that the given information does not provide specific details about individual scores or the overall grade distribution. It only tells us about the standard deviation, which is a measure of dispersion. To obtain a more complete understanding, it would be helpful to know the mean grade, the minimum and maximum scores, as well as the shape of the distribution (e.g., normal, skewed).