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Statistics Calculator

Math Calculators

Mean, median, mode, variance, standard deviation and quartiles

Quick Answer

Statistics Calculator: Mean, median, mode, variance, standard deviation and quartiles. Mean x̄ = Σxᵢ ÷ n · Median = middle value · Mode = most frequent.

Paste numbers separated by comma / space / newline. Sample stats use N−1 (Bessel correction).
Mean19.6250
Median19.0000
Mode15
Sample SD (N−1)5.9266
Population SD (N)5.5439
Sample variance35.1250
Population variance30.7344
Range18.0000
Count8
Min12.0000
Max30.0000
Sum157.0000
Geometric mean18.8644

Step-by-step

  1. 1Count n = 8, sum = 157.0000
  2. 2Mean = sum ÷ n = 157.0000 ÷ 8 = 19.6250
  3. 3Sorted: 12.0000, 15.0000, 15.0000, 18.0000, 20.0000, 22.0000, 25.0000, 30.0000
  4. 4Median = (18.0000 + 20.0000) ÷ 2 = 19.0000
  5. 5Σ(x−x̄)² = 245.8750
  6. 6Sample variance = Σ(x−x̄)² ÷ (n−1) = 245.8750 ÷ 7 = 35.1250
  7. 7Sample SD = √35.1250 = 5.9266
  8. 8Mode = 15

Empirical rule (68–95–99.7)

RangeBounds (sample SD)Approx. coverage
x̄ ± 1σ13.70 ~ 25.5568%
x̄ ± 2σ7.77 ~ 31.4895%
x̄ ± 3σ1.85 ~ 37.4099.7%
Mean vs median: the mean is pulled toward outliers (income data is the classic case), while the median is robust. If the two differ greatly, report the median. Use sample SD (N−1) when your data is a sample of a larger population; population SD (N) only when you have every member.

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How to Use

  1. Enter values or expressions: type directly into the Statistics 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

  • Statistics 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: Mean, median, mode, variance, standard deviation and quartiles.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Descriptive statistics (x₁…xₙ)

Mean x̄ = Σxᵢ ÷ n · Median = middle value · Mode = most frequent
Population variance σ² = Σ(xᵢ−x̄)² ÷ n · Sample variance s² = Σ(xᵢ−x̄)² ÷ (n−1)
Std dev = √variance · Range = max − min

FAQ

How do I use the Statistics Calculator?
Open the page and fill in the input fields — results update automatically. Mean, median, mode, variance, standard deviation and quartiles.
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. Statistics Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/statistics

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