Describe the set of scores in a sample with a mean of M = 40 and a standard deviation of SD = 4. (Where are most of the scores located? Where are they centered? What range of values do they cover?)

Answer 1

The "mean" is another way of saying "the average". So if 40 is your mean score, it's your average score. This suggests that most scores fall near and around 40. If the standard deviation is 4 most score would fall between 36 and 44. They would be centered around that 40 mark. One standard deviation would be 4 points in either direction. The standard deviation is a measure of the amount of variation or dispersion of a set of values. An SD of 4 is considered a low standard deviation so that's how you know that most scores will fall around the mean score (40).