Sample Size for a Mean
Plan sample size from assumed population deviation and desired error.
Your numbers
Required sample size
Normal approximation for simple random sampling. The assumed deviation must come from relevant evidence.
Scenario comparison
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Formula
Use n₀ = (zσ/E)². σ is assumed population deviation, E is desired half-width, and z is the two-sided normal critical value. For finite population N, use n = n₀/[1+(n₀−1)/N]; otherwise keep the uncorrected value. Round up to a whole sample count.
Plan sample size from assumed population deviation and desired error.
Worked example
- Assumed population standard deviation
- 10
- Desired half-width
- 2
- Confidence level (%)
- 95
- Finite population, zero for unlimited
- 0
- Required sample size
- 97
Scope and limitations
Normal approximation for simple random sampling. The assumed deviation must come from relevant evidence.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: f2b649c142e4 · Example checked: