Normal mean evidence update
Update a normal prior with a mean whose sampling variance is known.
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The fourth field is the known population SD of individual observations, not the standard error. n must be a positive whole number. Both SDs must be positive.
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Posterior mean
- 0.8
- Posterior SD
- 0.89442719
- 95% credible lower
- -0.95304508
- 95% credible upper
- 2.5530451
How to interpret the output
Normal likelihood with known variance and a normal prior gives a precision-weighted posterior mean. The credible interval conditions on the prior and known variance; substituting an estimated SD understates variance uncertainty. Use only for teaching or justified known-variance settings.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.