How to use the chebyshev inequality calculator
Find the most data that can lie more than k standard deviations from the mean, for any distribution. Enter number of standard deviations k in the field above; the maximum share outside k standard deviations, minimum share within k standard deviations are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “Chebyshev inequality”, “bound on outliers”, “how much data is beyond k sigma”, “calculate chebyshev inequality”, “find maximum share outside k standard deviations”.
Formula
Variables
- k — Number of standard deviations k
Worked example
With number of standard deviations k = 3, the calculator gives maximum share outside k standard deviations ≈ 11.11111 %; minimum share within k standard deviations ≈ 88.88889 %.
Frequently asked questions
What is the chebyshev inequality calculator used for?
Find the most data that can lie more than k standard deviations from the mean, for any distribution. It helps with questions such as “Chebyshev inequality”, “bound on outliers”, “how much data is beyond k sigma”.
What is the formula for the chebyshev inequality calculation?
Maximum share outside k standard deviations (%) = 100 / (k × k). Minimum share within k standard deviations (%) = 100 × (1-1 / (k × k)). Here k is number of standard deviations k.
What inputs do I need for the chebyshev inequality calculator?
You need number of standard deviations k. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the chebyshev inequality calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the chebyshev inequality result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.