Chebyshevs Theorem Calculator

Choose 1 of the 2 below:
What is the that x is within standard deviations of the mean
The probability that X is k standard deviations of the mean is

How does the Chebyshevs Theorem Calculator work?

Using Chebyshevs Theorem, this calculates the following:
Probability that random variable X is within k standard deviations of the mean.
How many k standard deviations within the mean given a P(X) value.
This calculator has 2 inputs.

What 1 formula is used for the Chebyshevs Theorem Calculator?

  1. P(|X - μ|) ≥ kσ) ≤ 1/k2

For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Chebyshevs Theorem Calculator?

absolute value
A positive number representing the distance from 0 on a number line
chebyshevs theorem
estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.
P(|X - μ|) ≥ kσ) ≤ 1/k2
A statistical measurement also known as the average
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
A statement provable using logic

Chebyshevs Theorem Calculator Video