Range

The range is the difference between a dataset's maximum and minimum values — the simplest possible measure of spread, computed directly from the two values that bound the data, with no averaging or weighting of anything in between. Its simplicity is also its principal limitation: because the range depends on exactly two values out of an entire dataset, it ignores everything about how the rest of the data is actually distributed between those two extremes, which makes it an easy statistic to compute and an easy one to be misled by if used as the only measure of spread.

Two datasets can share an identical range while looking completely different in how their values are actually distributed — one tightly clustered with a single far-flung outlier at each end, another spread out roughly evenly across the full span — and the range alone cannot distinguish between them, since it only ever reflects the two most extreme points, never the shape or density of everything in between. This is the exact same structural weakness that makes the mean sensitive to outliers, but worse: where the mean at least incorporates every value in its calculation (even if unevenly weighted toward extremes), the range incorporates only two values out of the entire dataset and discards all information about the rest entirely.

This is precisely why the range is rarely used as a dataset's primary or sole measure of spread in rigorous statistical reporting, and why the interquartile range (the span between the 25th and 75th percentile) and the standard deviation exist as more robust alternatives — both incorporate information about where the bulk of the data actually sits rather than only its two most extreme points, and both are considerably less distorted by a single unusual outlier at either end. The range's extreme sensitivity to outliers also mirrors and compounds its sensitivity to sample size: a larger sample has more opportunities to produce both a lower minimum and a higher maximum purely by chance, which means the range tends to grow with sample size even when drawn repeatedly from the exact same underlying population — a behavior it shares with, and inherits directly from, the minimum and maximum it's built from.

Despite these limitations, the range retains genuine practical value specifically because of how cheap and immediate it is to compute and interpret: in quality control and manufacturing, the range of a small sample (a range chart, part of statistical process control methodology developed by Walter Shewhart in the 1920s at Bell Labs) is still widely used as a fast, easily understood proxy for process variability on the shop floor, precisely because it requires no statistical training to compute or explain to a non-technical operator, unlike standard deviation, whose formula is considerably less intuitive to someone without a statistics background.

Read the range as the simplest and cheapest measure of spread available, and recognize its tradeoff clearly: its ease of computation and interpretation is exactly why it remains in practical use in contexts like manufacturing quality control, while its complete disregard for everything between the two extreme values is exactly why it's rarely treated as a sufficient or rigorous measure of spread on its own, with the interquartile range and standard deviation existing specifically to capture what the range, by design, leaves out.