Standard deviation

Standard deviation translates variance back into the variable's units. A sample standard deviation of 6 days describes invoice-to-invoice spread in days, not squared days.

What it does—and does not—say

Standard deviation uses every observation and gives greater influence to values farther from the mean. Juniper's 78-day invoice therefore increases Year 2's sample standard deviation sharply. The result accurately describes the supplied sample under the declared n - 1 convention. It does not decide whether 78 is erroneous or predict how often future invoices will be late.

Statements such as “most observations fall within two standard deviations” need a distributional basis. That familiar rule fits an approximately normal model; it is not guaranteed for an arbitrary business distribution.

Do not confuse two kinds of spread

Standard deviation describes variation among observations. The standard error of the mean describes estimated variation among sample means under repeated sampling. They have related formulas but different objects. More observations can reduce standard error while the underlying invoice-level standard deviation remains similar.

When comparing groups or periods, align variable definitions, units, selection designs, and denominator conventions. A larger standard deviation is a descriptive difference, not automatically greater financial risk or worse operating control.