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Standard Deviation Calculator

Math Calculators

Population/sample SD, variance, CV, SEM

Quick Answer

Standard Deviation Calculator: Population/sample SD, variance, CV, SEM. Standard Deviation Calculator uses standard math formulas to compute accurate results instantly.

Data set (comma / space / newline separated)

Sample standard deviation s
2.13809
Population σ = 2.00000
Mean5.00000
Sample variance s²4.57143
Std error SEM0.755929
CV42.76%

Calculation steps

  1. 1n = 8, sum = 40.00
  2. 2Mean x̄ = 40.00 ÷ 8 = 5.0000
  3. 3Sum of squared deviations Σ(x−x̄)² = 32.0000
  4. 4Population: σ² = Σ(x−x̄)² ÷ n = 4.0000 → σ = 2.0000
  5. 5Sample: s² = Σ(x−x̄)² ÷ (n−1) = 4.5714 → s = 2.1381
  6. 6SEM = s ÷ √n = 0.7559; CV = s ÷ |x̄| × 100% = 42.76%

Population σ vs sample s

ScenarioDivisorExample
Whole population datan (σ)Heights of all 30 students in the class
Sample to estimate populationn−1 (s)Inspect 100 bulbs to estimate the whole batch
Bessel correctionn−1Unbiases variance; s is always slightly larger than σ
CV (coefficient of variation) compares dispersion across different units/scales: <10% low, 10–30% moderate, >30% high. In a normal distribution, ~68% of data lies within ±1σ, ~95% within ±2σ.

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How to Use

  1. Enter values or expressions: type directly into the Standard Deviation Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Standard Deviation Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Population/sample SD, variance, CV, SEM.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Standard Deviation Calculator formula

Standard Deviation Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Standard Deviation Calculator?
Open the page and fill in the input fields — results update automatically. Population/sample SD, variance, CV, SEM.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

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Cite this page: YiJianSuan. Standard Deviation Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/standard-deviation

Results provided by this tool are for reference only and do not constitute professional advice.