How to Calculate Chebyshev's Inequality Theorem for Probability - Tutorial

How to Calculate Chebyshev's Theorem - Definition, Formula, Example

Definition:

Chebyshev's inequality also called as Chebyshev’s Theorem. It defines that at least 1-1/K2 of data from a sample must fall down within K standard deviations from the mean, where K is any positive real number larger than one.

Formula:

Probability P(X-μ<2σ) = 1 - (1/K2)
Where,

K = Standard Deviation

Example :

Daily students study for an average time of 4 hours with standard deviation of 15 minutes. Calculate the fraction value if the students study between 3 and 5 hours?

Given,

Standard Deviation (K) = 4

Solution :

The mean time is one hour. [3 to 5 hours, where the average mean is one hour] One hour corresponds to four standard deviation (K) = 4 [60min/15min] P(X-μ<2σ) = 1 - (1/42) P(X-μ<2σ) = 1 - (1/16) P(X-μ<2σ) = 1 - 0.0625 P(X-μ<2σ) = 0.9375 So, Chebyshev's inequality says that at least 93.75% of the data values of any probability distribution must be within 4 standard deviations of the mean.

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