Sample and population standard deviation: why the denominator matters
A standard deviation describes dispersion around a mean using squared deviations.
Name the quantity being summarized
A standard deviation describes dispersion around a mean using squared deviations. Two common formulas differ in their denominator: the population version divides the sum of squared deviations by N, while the sample version uses N minus 1. A spreadsheet result cannot be checked properly until you know which definition was selected and which rows were included.
Outcomes 2, 4 and 6 have mean 4. The two horizontal spans show one population standard deviation (about 1.633) and one sample standard deviation (2) on either side, not confidence intervals.
Open full-size diagram ↗Work through three invented outcomes
Take outcomes of 2, 4 and 6 units. Their mean is 4. Deviations are minus 2, zero and plus 2, whose squares total 8. Population variance is 8 / 3 and population standard deviation is approximately 1.633. Sample variance is 8 / 2 = 4 and sample standard deviation is 2.
Worked example: Population standard deviation: 1.63299; Sample standard deviation: 2. Invented values; units follow the row labels and article.
Open full-size diagram ↗Do not confuse variance with standard deviation
Variance is expressed in squared units; standard deviation returns to the original unit after taking the square root. For a one-observation dataset, the sample denominator is zero, so the usual sample standard deviation is undefined. Entering zero would falsely suggest that dispersion has been meaningfully estimated.
Calculation checklist: Observations: 2, 4, 6; Squared deviations total: 8; Denominators: N = 3; N - 1 = 2. Preserve these definitions when reproducing the example.
Open full-size diagram ↗Keep interpretation within the evidence
Record the formula, row count, units and missing-value policy. A cash-outcome deviation can change with position size and should not be casually compared with a percentage-return deviation. These three invented numbers demonstrate calculation only. A sample estimate is not a guaranteed future range, and no normal-distribution probability claim follows merely from calculating a mean and standard deviation.
Sources and conventions
Examples are hypothetical. Worked examples state their formulas and assumptions in the article; our methodology explains the related calculators. Broker contract specifications determine actual lot, margin and execution conditions. These sources document definitions and data; a source link does not imply endorsement of SanForex or a trading service.
These materials are prepared with AI assistance and checked against worked examples and deterministic calculation tests where applicable. They are not an expert suitability assessment or investment advice.
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