How it works
σ uses n; s uses n−1. SEM ≈ s/√n. Margin of error ≈ z·SEM at your confidence level. Variance is std dev squared.
σ=√(SSD/n) · s=√(SSD/(n−1)) · MOE≈z·SEM
When to use
Use this tool when you need to: try 10, 12, 23, 23, 16, 23, 21, 16 — mean 18, s ≈ 5.24, SEM ≈ 1.85, 95% MOE ≈ ±3.63. Or 1,3,4,7,8 for population σ ≈ 2.58.
How to use this tool
- Enter your values in the fields above.
- Review the formula and any mode options for your problem.
- Read the result and the step-by-step solution.
Try 10, 12, 23, 23, 16, 23, 21, 16 — mean 18, s ≈ 5.24, SEM ≈ 1.85, 95% MOE ≈ ±3.63. Or 1,3,4,7,8 for population σ ≈ 2.58.
Frequently asked questions
- What is the Standard Deviation Calculator?
- σ uses n; s uses n−1. SEM ≈ s/√n. Margin of error ≈ z·SEM at your confidence level. Variance is std dev squared.
- How do I use the Standard Deviation Calculator?
- Enter the required values, then calculate. The Standard Deviation Calculator shows results, formulas, and step-by-step work when available. No account is required.
- What formula does the Standard Deviation Calculator use?
- σ=√(SSD/n) · s=√(SSD/(n−1)) · MOE≈z·SEM
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