Q. 3.144 - Elementary Statistics

Question

What does Chebyshev's rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer. 

Step-by-Step Solution

Answer

Chebyshev’s Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean.  

Step 1: Given Information

We need to discuss about the percentage of observations that lie within one standard deviation to either side of the mean according to Chebyshev's rule.

Step 2: Explanation

Chebyshev's Theorem is used to determine the lowest proportion of observations that fall within a given number of standard deviations from the mean. For a wide range of probability distributions, this theorem holds. Another term for it is Chebyshev's Inequality.

Chebyshev's Theorem can help us figure out where the majority of the data in a value distribution falls. This theorem gives beneficial results when we just have the mean and standard deviation. We don't need to know how our data is distributed.

According to the rule of Chebyshev, at least $100\left(1-\frac{1}{k^2}\right)\%$ of the data values is within k standard deviations from the mean $(k>1)$.