What measure describes the average distance of every score from the mean and is also known as standard error?

The concept being described in the question is centered around a statistical measure that quantifies the degree of variation or dispersion in a set of data points relative to the mean. In this case, the standard deviation is the correct answer because it specifically measures the average distance that each data point deviates from the mean of the dataset.

Standard deviation is critical in statistics because it provides insight into the consistency of data – a low standard deviation indicates that the scores tend to be close to the mean, while a high standard deviation suggests that the scores are spread out over a broader range of values. The connection between standard deviation and standard error is also significant; standard error is derived from the standard deviation of a sample, reflecting how accurately the sample mean estimates the population mean.

The other terms may refer to related concepts but do not directly address the average distance from the mean in the same way. Mean deviation refers to the average of absolute differences from the mean, whereas "data spread" is a more general term that does not have a precise statistical definition. Sample error pertains to the discrepancy between a sample statistic and the actual population parameter, which is distinctly different from measuring variance or deviation about the mean.