What Chebychev is
In statistics, Chebychev’s theorem is a result about the distribution of values taken by a random variable in a given interval. It states that for any real number k > 0, the proportion of values taken by a random variable within k standard deviations of its mean is at least 1 - (1/k2).
Steps for Chebychev:
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Calculate the mean (μ) and standard deviation (σ) of the data.
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Calculate the value of k, which is the number of standard deviations away from the mean.
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Calculate the lower and upper bounds of the interval by subtracting and adding kσ from the mean, respectively.
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Calculate the proportion of values falling within the interval (1 - (1/k2)).
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Compare the calculated proportion to the actual proportion of values falling within the interval. If the calculated proportion is greater, then Chebychev’s theorem is satisfied.
Examples
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Chebychev’s Inequality can be used to calculate the probability that a random variable is within a certain distance from its mean.
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Chebychev’s Inequality can be used to bound the probability of a given event.
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Chebychev’s Inequality can be used to calculate the probability that a random variable is within a certain range of values.