Chebyshev’s Rule Calculator

Instructions: This Chebyshev's Rule calculator will show you how to use Chebyshev's Inequality to estimate probabilities of an arbitrary distribution. You can estimate the probability that a random variable $$X$$ is within $$k$$ standard deviations of the mean, by typing the value of $$k$$ in the form below; OR specify the population mean $$\mu$$, population standard deviation $$\sigma$$ and the even $$(a,b)$$ for which you want to estimate the probability:

Type of the value of k (number of standard deviations from the mean)

OR:
Population Mean ($$\mu$$)
Population St. Dev. ($$\sigma$$)
Lower Limit of the event $$(a)$$:
Upper Limit of the event $$(b)$$:

More About the Chebyshev's Inequality Calculator

We use Chebyshev's inequality to compute the probability that $$X$$ is within $$k$$ standard deviations of the mean. According to Chebyshev's rule, the probability that $$X$$ is within $$k$$ standard deviations of the mean can be estimated as follows:

$\Pr(|X - \mu| < k \sigma) \le 1 - \frac{1}{k^2}$

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.