Which measure indicates how far, on average, individual data points deviate from the mean?

The correct choice is standard deviation, as it specifically quantifies the amount of variation or dispersion of a set of values. It calculates how much individual data points deviate from the mean of the dataset in a standardized way. The standard deviation is derived by taking the square root of the variance, providing a measure of spread that is in the same units as the original data.

By using the standard deviation, you can assess the average distance of data points from the mean, giving a sense of how clustered or spread out the data values are. This metric is particularly useful in various statistical analyses, especially when comparing variability between different datasets.

Other measures, like variance, also provide insights into data dispersion but do so in squared units, which can make interpretation less intuitive. The range indicates the difference between the maximum and minimum values, providing no insight into how individual data points are distributed around the mean. Mean absolute deviation also measures average dispersion, but standard deviation is widely used as it incorporates the square root function, allowing it to reflect the distribution of the data points more effectively.