Mean, Median, Geometric & Harmonic Mean Calculator

Compare arithmetic, geometric, and harmonic means alongside median and range.

Arithmetic Mean (x̄)
36
Median (Q₂) 30
Geometric Mean (G) 28.619
Harmonic Mean (H) 22.642
Dataset Range (Max − Min) 70
Inputs
First value x₁.
Second value x₂.
Third value x₃.
Fourth value x₄.
Fifth value x₅.
Results & Graph
Arithmetic Mean (x̄)
36
Median (Q₂)
30
Geometric Mean (G)
28.619
Harmonic Mean (H)
22.642
Dataset Range (Max − Min)
70

Arithmetic Mean (x̄)

Graph 1 • Value1 Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 20.0 40.0 50%: 35 35 50% 75%: 35.5 35.5 75% 100%: 36 36 100% 125%: 36.5 36.5 125% 150%: 37 37 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Arithmetic Mean (x̄) 36 Median (Q₂) 30 Geometric Mean (G) 28.619 Harmonic Mean (H) 22.642
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Arithmetic Mean (x̄)36Median (Q₂)30Geometric Mean (G)28.619Harmonic Mean (H)22.642Dataset Range (Max − Min)70
Summary: Mean = 36, Median = 30, Geometric Mean = 28.619, and Harmonic Mean = 22.642 (satisfying H ≤ G ≤ A).
Summary: Mean = 36, Median = 30, Geometric Mean = 28.619, and Harmonic Mean = 22.642 (satisfying H ≤ G ≤ A).

Formula & Mathematical Methodology: Mean & Median Mathematical Identity

x̄ = (Σxi)/n
G = (Πxi)1/n
H = n / Σ(1/xi)
x̄ = (Σx_i)/n; G = (Πx_i)^(1/n); H = n / Σ(1/x_i)
  • value1: Value1 (numeric parameter)
  • value2: Value2 (numeric parameter)
  • value3: Value3 (numeric parameter)
  • value4: Value4 (numeric parameter)
  • value5: Value5 (numeric parameter)

Rounding: All calculations run in double-precision IEEE-754 arithmetic; displayed outputs round to up to 4 decimal places.

Worked Example: Worked Mathematical Verification: Mean & Median

Compare arithmetic, geometric, and harmonic means alongside median and range.

  1. Verify the domain constraints of the input parameters.
  2. Apply the governing mathematical identity: x̄ = (Σx_i)/n; G = (Πx_i)^(1/n); H = n / Σ(1/x_i).
  3. Cross-check the primary value against the supporting invariants and coordinate graph.
Result: Evaluates Mean & Median via x̄ = (Σx_i)/n; G = (Πx_i)^(1/n); H = n / Σ(1/x_i).

Frequently Asked Questions

What mathematical formula does the Mean, Median, Geometric & Harmonic Mean Calculator use?

It directly evaluates x̄ = (Σx_i)/n; G = (Πx_i)^(1/n); H = n / Σ(1/x_i) in double-precision floating-point arithmetic and updates all supporting invariants and graphs live.

How can I compare different parameter sets?

Click Compare in the results toolbar to pin up to three parameter combinations side by side.

Can I export the mathematical report or share a link?

Yes. Use the Share Link, Copy Summary, or Markdown/JSON export buttons in the results panel.

Mathematics & Statistics • Descriptive Statistics Guide

How to Use the Mean, Median, Geometric & Harmonic Mean Calculator: Practical Guide & Visual Analysis

Calculate arithmetic mean, median, midrange, range, geometric mean, and harmonic mean of a dataset. Includes textbook mathematical notation, step-by-step verification, and three custom SVG visualizations. Whether you are researching mean, median, geometric & harmonic mean calculator, mean & median, mean median mode range, descriptive statistics calculator, this interactive tool helps you calculate arithmetic mean, median, midrange, range, geometric mean, and harmonic mean of a dataset.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust Value1, Value2, Value3, Value4, the calculator immediately computes Primary exact or numerical solution, Supporting identities & invariants, 3-Panel mathematical SVG plots and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Universal Mathematical & Statistical Standard (ISO 80000-2))

In our benchmark scenario (Worked Mathematical Verification: Mean & Median), Evaluates Mean & Median via x̄ = (Σx_i)/n; G = (Πx_i)^(1/n); H = n / Σ(1/x_i). Keep in mind that uses standard Euclidean geometry, real/complex algebra, and NIST statistical definitions. For related calculations in Mathematics & Statistics, explore Scientific Calculator, Statistics & Standard Deviation Calculator, Geometry Calculator (Right Triangle, Circle & Cylinder).