Chebyshev's theorem states that: i. About 68% of the observation will lie within one standard deviation of the mean.
ii. About 95% of the observations will lie within two standard deviations of the mean.
iii. Virtually all (99.7%) will lie within three standard deviations of the mean.
A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements, but not (i).
E) (i), (ii) and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Chebyshev's theorem actually states that for any dataset, regardless of distribution, at least $1-\frac{1}{k^2}$ of the data within $k$ standard deviations from the mean, for any $k>1$. Statements (i), (ii), and (iii) describe the empirical rule, which applies specifically to normal distributions, not Chebyshev's theorem.

Chebyshev's Theorem States That: I