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Sampling Standard Error Calculator — result sheet
Calculate the standard error of a sample mean and an illustrative 95% normal-approximation margin.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: SE = s/√n; illustrative 95% normal margin = 1.96 × SE.
Standard error describes the modeled variability of a sample mean under repeated sampling. The optional 1.96 margin is a normal approximation, not a universal confidence interval rule.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample standard deviation — minimum 1.0E-6; maximum 1000000000
- Sample size n — minimum 2; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Sample standard deviation | 12 |
| Sample size n | 36 |
Standard error: 2; illustrative 95% margin: 3.92.
Assumptions and limits
- The sample standard deviation is positive and uses the sample convention; n is a whole number of at least two.
- The 1.96 margin assumes a two-sided normal approximation and should be replaced by a suitable critical value when needed.
- Standard error is not the standard deviation of individual observations and is not a measure of data quality by itself.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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