What statistical measure indicates how much, on average, the scores differ from the mean?

The statistical measure that indicates how much, on average, the scores differ from the mean is the standard deviation. This measure is vital in statistics because it provides insight into the spread or dispersion of a set of values in relation to the mean. Specifically, the standard deviation quantifies how much the individual scores in a data set typically deviate from the average score.

The standard deviation is widely used because it reflects the degree to which the individual data points differ from the mean, allowing for a clearer understanding of variability within the data. A larger standard deviation indicates greater variability amongst the data points, while a smaller standard deviation suggests that the scores are closer to the mean.

Variance is indeed related but not quite the same; it measures the average of the squared differences from the mean. While both variance and standard deviation convey similar information regarding variability, standard deviation is more intuitive because it is in the same units as the original data, making it easier to interpret.

The range reflects the difference between the highest and lowest scores in a data set but does not provide information about how the scores are spread around the mean. The mean absolute deviation also measures how much scores deviate from the mean, but it does so in terms of absolute values rather than standardizing those deviations