Using Chebyshev's theorem for standard deviation, calculate the percentage of data that lie within five standard deviations of the mean.
A) 89%
B) 75%
C) 96%
D) 50%

Question

Quizplus · Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of the data lies within k standard deviations of the mean, where k is any positive integer greater than 1. Therefore, when k = 5, at least (1 - 1/5^2) = 96% of the data lies within 5 standard deviations of the mean. Therefore, the best choice is C, with a percentage of 96%.

Using Chebyshev's Theorem for Standard Deviation, Calculate the Percentage of Data