When using Chebyshev's Theorem, the minimum percentage of sample observations that will fall within two standard deviations of the mean will be __________ the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule).
A)smaller than
B)greater than
C)the same as

Question

Quizplus · Accepted Answer

Chebyshev's theorem is a more general rule than the empirical rule that applies to all distributions, while the empirical rule applies only to normal distributions. Chebyshev's theorem states that at least (1 - 1/k^2) of the data will fall within k standard deviations of the mean, where k is any number greater than 1. Therefore, the minimum percentage of sample observations that will fall within two standard deviations of the mean using Chebyshev's theorem is 1 - 1/2^2 = 75%. This is smaller than the percentage within two standard deviations if a normal distribution is assumed, which is approximately 95% (or 99.7% within three standard deviations).

When Using Chebyshev's Theorem, the Minimum Percentage of Sample Observations