Spread of a distribution

Spread, also called variability, is how far apart the values in a distribution sit. The Fall 2026 course names three measures. The range is maximum minus minimum. The interquartile range is $\text{IQR} = Q_3 - Q_1$, the width of the middle half. The standard deviation $s$ is a typical distance of a value from the mean. Report the one that matches your center: the mean travels with $s$, the median travels with the IQR.

Two five-value sets, 0, 5, 5, 5, 10 and 0, 0, 5, 10, 10, share a mean of 5, a median of 5, and a range of 10, and they do not look alike. The first has $s = 3.54$ and $\text{IQR} = 5$. The second has $s = 5.00$ and $\text{IQR} = 10$, because everything in it has been pushed out to the ends.

"Both sets run from 0 to 10, so they are equally spread out." The range knows only the two extremes, so it cannot tell those sets apart, and it can never shrink when you add another observation. The IQR and the standard deviation read the values in between, which is exactly why they separate 3.54 from 5.00 where the range reports 10 twice.

One caution on the IQR. This site and the TI-84 locate quartiles by the median-excluded rule, dropping the overall median from both halves when $n$ is odd. Other software uses a different rule and can return a slightly different $Q_1$ and $Q_3$ from identical data, so a mismatch with a spreadsheet is usually a convention difference rather than an arithmetic error.

Spread appears in topic 1.6 of the Fall 2026 course as one of the features a description has to cover, and in topic 1.7 as a calculation, where all three measures are named. Topic 1.9 asks you to compare it across groups, and that comparison has to be written explicitly: say that one distribution is more variable than the other and quote both numbers, rather than describing each group in its own sentence and leaving the reader to do the subtraction.