According to the Chebyshev rule,at least 93.75% of all observations in any data set are contained within how many standard deviations around the mean?
A)1
B)2
C)3
D)4

Question

Quizplus · Accepted Answer

Chebyshev's rule states that at least $1 - \frac{1}{k^2}$ of the data within a data set will fall within $k$ standard deviations from the mean. For at least 93.75% of the data to be within a certain number of standard deviations, we set $1 - \frac{1}{k^2} = 0.9375$. Solving for $k$ gives $k = 4$, meaning at least 93.75% of the data is within 4 standard deviations of the mean.

According to the Chebyshev Rule,at Least 93