What is a more reliable indicator of the spread of a distribution that determines score deviations from the mean?

The standard deviation is the most reliable indicator of the spread of a distribution for determining score deviations from the mean. It measures the average distance of each data point from the mean, providing insight into how much individual scores vary from the average. A lower standard deviation indicates that scores tend to be closer to the mean, while a higher standard deviation signifies that scores are spread out over a wider range.

This measure is particularly useful in assessing the dispersion of data in normally distributed datasets, as it takes into account all data points rather than just the highest and lowest (as the range does). Standard deviation is also crucial for further statistical analyses as it is used in calculating confidence intervals and in various hypothesis testing scenarios.

In contrast, while variance also measures dispersion, it does so in squared units, which can make interpretation less straightforward. The range, being merely the difference between the highest and lowest values, can provide a limited view of distribution spread and is sensitive to outliers. The median indicates the central tendency but does not provide information about the spread of scores. Therefore, standard deviation is the most comprehensive and efficient measure for understanding score deviations relative to the mean.