Question
Put variation beside the average
Five minutes on average can mean five minutes every time—or an unpleasant lottery.
When it fits
- Two options share the same mean but may differ in reliability.
When to avoid it
- Do not apply normal-distribution coverage rules merely because a standard deviation has been calculated.
A question to ask
How much do ordinary observations vary? · Are rare extremes important to the decision? · Would a distribution or quantile summary reveal what one spread number hides?
Why it matters
Look at the spread as well as the centre. Range reveals extremes; standard deviation summarizes dispersion around the mean; an interquartile range focuses on the middle half. Choose a description that makes the decision-relevant variability visible.
An example
Durations of 4, 5 and 6 minutes and durations of 0, 5 and 10 minutes both average 5, but offer different predictability.
Check your result
The comparison includes variability relevant to the user's experience or operational risk.
Keep this limit in mind
- Do not apply normal-distribution coverage rules merely because a standard deviation has been calculated.
Evidence and sources
Range and standard deviation describe different aspects of variation, which a mean alone cannot identify.
A spread measure does not by itself explain the source of variation or establish a normal distribution.
Introductory Statistics 2e, 2.7: Measures of the Spread of the Data · Definitions of range and standard deviation