In statistics, Chebyshev's theorem asserts that for most probability distributions, not more than 1/k² of measured data would be k standard deviations from the mean.
Chebyshev's Theorem calculates the proportion the observations which fall within a fixed number of the mean standard deviations. This theorem holds true for a diverse range various probability distributions. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Chebyshev's theorem states that the shaded area in the diagram is equal to 1 - 1/k² so because area that under probability distribution curve equals equal to 1.
The shaded area shown in the diagram is when k = 1.75.
1 - 1/1.75² = 0.35
1 - 1/1.75² = 67.35%
As a result, the percentage of the area within +/-1.75 standard deviations of the mean is;
67.35/2 = 33.7%,
33% is the least for the observation.
Therefore, the Chebyshev theorem states that at least 33% of a observations are inside +/- standard deviations of the mean.
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