CALCULATE WITH CONFIDENCE

Averages & Means

Mean Comparison Calculator

Compare harmonic, geometric, arithmetic, and root mean square values on one dataset.

Averages & Means

Compare four classical means

H ≤ G ≤ A ≤ RMS
Positive values

Use ordinary decimals; blank rows are ignored.

Mean ordering

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Enter strictly positive values so all four means are defined.
  2. Inspect each result and the H≤G≤A≤RMS ordering.
  3. Choose the mean based on the quantity's meaning, not merely its numerical position.

Calculation method

Evaluate four distinct averaging relationships

The same data are processed through reciprocal, multiplicative, additive, and squared relationships. Equality throughout occurs exactly when all entered values are equal.

Worked example

Compare 1 and 4

The means separate because the inputs differ.

H=1.6 ≤ G=2 ≤ A=2.5 ≤ RMS≈2.915

Supported inputs

Precision and limits

List size

Add 1–100 labelled value rows.

Decimal size

Each value may contain up to 200 digits and 100 decimal places.

Exactness

Exact rational results are never replaced by a rounded decimal; approximations are labelled.

Domain

All values must be strictly positive for a complete four-mean comparison.

Decision boundary

The ordering theorem does not determine which mean matches a real-world estimand.