SD quantifies how far scores scatter from the mean—the backbone of curves, bands, reliability and benchmark width.
Standard deviation is the typical distance between scores and their mean. Small SD means the group agrees; large SD means the label "average" is hiding several different populations.
σ = √( Σ(x − μ)² / N ) (population); sample uses n−1.
Two cohorts both average 3.8/5 satisfaction: one SD .4 (uniform win), one SD 1.2 (polarized—read the comments before celebrating).
Report it beside every mean you publish; use it for SD-based letter bands, control charts and benchmark width.
SD is meaningless on a single time point of skewed or bimodal data—and n−1 vs n must be stated for small samples.
Range reads two numbers but ignores everyone in between; SD uses every response—prefer SD, show range as footnote.
Bessel's correction: sample means chase the data, so dividing by n underestimates spread. For n>30 the difference is cosmetic.
Turn the concept into a live assessment：Standard Deviation
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