How does the Empirical Rule work and how does it relate to the bell curve as illustrated in Figure 3.14 (a)? Then, explain Chebyshev's Theorem and how it is different from the Empirical Rule. Give a specific example of a population with which the Empirical Rule might be most effective and one with which Chebyshev's Theorem might be most effective.
Please take a look at the attached document for a description on the Empirical Rule.© BrainMass Inc. brainmass.com October 25, 2018, 7:17 am ad1c9bdddf
The Empirical Rule is a rule in statistics that says for a normal distribution, most of all of the data will land between three standardized, yet different, deviations from their mean. What the empirical rule does it, it displays that 68% of the information will fall inside the first standard deviation, that about 95% of the data will fall ...
Chebyshev's Theorem vs. Empirical Rule
In the following example, why would Chebyshev's Theorem be used instead of the Empirical Rule?
The Empirical Rule is a rule in statistics that says for a normal distribution, most of all of the data will land between three standardized yet different deviations from their mean. What the empirical rule does is it displays that 68% of the information will fall inside the first standard deviation, that about 95% of the data will fall within the first two standard deviations, and that 99.7% of the data will fall within the first three standard deviations of the mean. It is also sometimes called the rule of 68-95-99.7 of the 3 Sigma Rule.This rule very closely relates to the diagram (it displays the rule fairly accurately). Chebyshev's Theorem states essentially that a distribution of any shape or size puts a lower level on the percents of the observations. This occurs inside a provided number of standard deviations which come from its mean. Now the Empirical Rule on the other hand applies to more specifically mounded-shaped and or symmetrical distributions. It displays percentages as approximations inside of a standard deviation which comes from its mean. The Emperical Rule could apply to the gas mileage on Subaru Imprezzas and Chebyshev's Theorem could be used for something like trying to calculate what percentages of a value will end up between 159 and 227 for a data set with mean of 194 and standard deviation of 16.5.View Full Posting Details