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 for any dataset, regardless of distribution, at least $1 - \frac{1}{k^2}$ of the data values must be within $k$ standard deviations of the mean, where $k > 1$. For $k = 5$, this gives $1 - \frac{1}{5^2} = 1 - \frac{1}{25} = \frac{24}{25} = 0.96$, or 96%.

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