Chebyshevs Theorem Calculator

Publish date: 2024-06-16

Given a probability P that x is within k standard deviations of the mean, then k is denoted below:
k = √1/(1-P(x - μ < kσ)

Using your input of P(x - μ < kσ) = 0.75, let's plug in and evaluate:
k = √1/(1 - 0.75)
k = √1/0.25
k = √4

k = 2

What is the Answer?

How does the Chebyshevs Theorem Calculator work?

Free Chebyshevs Theorem Calculator - 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?

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 valueA positive number representing the distance from 0 on a number linechebyshevs theoremestimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.
P(|X - μ|) ≥ kσ) ≤ 1/k2meanA statistical measurement also known as the averageprobabilitythe 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 Outcomesstandard deviationa measure of the amount of variation or dispersion of a set of values. The square root of variancetheoremA statement provable using logic