The concept
Variability describes how far observations differ from one another or from a center. Range uses the highest and lowest values; standard deviation emphasizes squared distances from the mean before returning to the original units. The appropriate summary depends on whether you care about typical variation, unusual extremes, or both.
Worked example
A fictional shuttle service offers two routes. Route A's sampled trips take 19, 20, and 21 minutes; Route B's take 10, 20, and 30 minutes. Both average 20 minutes, but their ranges are 2 and 20 minutes. A traveler with a strict arrival deadline may reasonably prefer Route A. A report that ranks the routes by average time alone misses the reliability difference that matters to that traveler.
Limits and judgment
Range depends on only two observations and often grows as more cases are collected. A single extreme point can strongly affect standard deviation. Compare samples collected under similar conditions and inspect a graph when possible. A narrow distribution is not inherently better: consistently late service could be less useful than variable service with an acceptable chance of arriving on time.
FROM UNDERSTANDING TO ACTION
Put it to work.
Invent two five-number datasets with the same mean but different ranges.
RETRIEVE. REASON. REMEMBER.
Knowledge check.
Choose one answer for each question, then check your reasoning.
Sources & further reading.
Links support the core concepts or identify the book. Examples, exercises, and critical analysis are original Institute material. Source checks are not an independent expert review of every claim.
- NIST: Measures of Scale ↗
Statistical core concept; all numerical scenarios and interpretations are original instructional examples. Source reviewed 2026-10-19.