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Chebyshev Theorem Coverage Calculator — result sheet
Calculate the guaranteed minimum fraction within k standard deviations of a mean.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Minimum fraction within k standard deviations = 1−1/k².
The result is a lower bound that does not require a normal distribution, and it is reported as fraction and percentage.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of standard deviations k — minimum 1.000001; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Number of standard deviations k | 2 |
At least 75% lies within 2 standard deviations.
Assumptions and limits
- k is greater than one and the distribution has finite mean and variance.
- The result is a guaranteed inequality bound, not an estimate of the actual coverage.
- Shape, skew, tails, sample uncertainty, and finite-population corrections are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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