What is more stable than the range because it's based on the spread of scores through the center of the distribution?

The concept being described relates to statistical measures that assess dispersion or variability within a dataset. The quartile deviation, also known as the semi-interquartile range, provides a measure of variability that focuses on the middle 50% of the data, thus offering a stable indication of data spread around the center.

The quartile deviation calculates the difference between the first and third quartiles and then divides by two, allowing it to indicate how concentrated the data points are around the median. This approach inherently reduces the influence of outliers, making it a more robust measure compared to the full range, which can be heavily affected by extreme values. By concentrating on the interquartile range, the quartile deviation effectively assesses data stability and provides a clearer picture of the central tendency's reliability.

In contrast, other measures of dispersion like the mean deviation, standard deviation, and variance consider all data points, which may introduce more volatility when outliers are present. Hence, while they can be useful in various contexts, the quartile deviation's focus on the middle of the distribution lends it a particular robustness in measuring stability compared to the more extreme values impacting the range.