In its standard form, Chebyshev's theorem provides a lower bound on ________.
A) the number of observations lying within a certain interval
B) the number of observations lying outside a certain interval
C) the proportion (or percentage) of observations lying within a certain interval
D) the proportion (or percentage) of observations lying outside a certain interval

Question

Quizplus · Accepted Answer

Chebyshev's theorem provides a lower bound on the proportion (or percentage) of observations lying within a certain number of standard deviations from the mean. Specifically, it states that at least 1 - 1/k^2 of the observations will fall within k standard deviations from the mean, where k is any positive constant greater than 1. This means that the proportion of observations within an interval will always be at least as large as the value given by Chebyshev's theorem.

In Its Standard Form, Chebyshev's Theorem Provides a Lower Bound