A theorem that characterizes the dispersion of data away from its mean
Chebyshevís inequality puts an upper bound on the probability that an observation should be far from its mean. It requires only two minimal conditions: (1) that the underlying distribution have a mean and (2) that the average size of the deviations away from this mean (as gauged by the standard deviation) not be infinite.
The probability that an observation will be more than k standard deviations from the mean is at most 1/k2.(k square)
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