Standard deviation
Standard deviation is the square root of variance and measures dispersion in the original units of the data. Larger values indicate greater spread on the specified basis, but comparisons between different means or measurement scales need context. Use the same population or sample convention as the variance calculation. Standard deviation summarises variability; it does not prove a distribution is normal or by itself identify the probability of a particular outcome.
Worked example
For a population with values 2, 4 and 6, variance is 8 / 3, so standard deviation is √(8 / 3) = 1.633. Its unit is the original measurement unit, whereas variance uses squared units.
Common mistake
Taking the square root before averaging squared deviations or using normal-distribution percentage rules for any dataset.
Where it appears in your exams
| Qualification | Exam | Relationship | Period |
|---|---|---|---|
| ACCA | MA | Direct | September 2026–June 2027 |
| FIA | FMA | Direct | September 2026–June 2027 |
