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THE FEUTEX TOOLKIT

Cantelli One-Sided Tail Bound

Bound a one-sided deviation from the mean using variance alone.

Probability workspace● Runs in your browser
01 Your input
02 Your result
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FormulaUpper Tail Bound = variance/(variance+a**2)
Sources and model references

Made for real tasks

  • Bound a one-sided deviation from the mean using variance alone.
Explore step-by-step workflows →

Worked example

Inputs

Population variance
4 number
Positive distance above mean
3 number

Expected results

Upper Tail Bound
0.3076923077 probability

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter population variance, positive distance above mean.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "variance": 4,
  "a": 3
}

Accuracy and scope

One-sided upper bound, not an estimated tail probability. Requires finite population variance.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.