Chebyshev Theorem Calculator
Find the guaranteed minimum percentage within k standard deviations for any distribution with finite variance.
Formula
Minimum=100(1−1/k²)%; interval=μ±kσ, k>1.
Guaranteed minimum ≈ 100×(1-1÷(2)^2) · Lower endpoint ≈ (100)-(2)×(15) · Upper endpoint ≈ (100)+(2)×(15)
How to use
- Enter the mean and positive standard deviation.
- Choose k greater than 1.
- Read the minimum percentage and interval.
Examples
- μ=100, σ=15, k=2 guarantees at least 75% within 70 to 130.
Frequently asked questions
Must data be normal?
No. The theorem holds for distributions with finite mean and variance.
Is this the exact percentage?
No. It is a lower bound; the actual percentage can be larger.
Are interval endpoints included?
The guarantee also holds for the closed interval shown. Use the same unit for mean and SD.
Sources
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