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The Empirical Rule in Statistics

The empirical rule is one of the basic statistical terms associated with the normal distribution. Also called the three-sigma rule, this law states that for a normal distribution, virtually all observable data will be within three standard deviations (Hayes, 2021). There is a ratio of 68-95-99.7, according to which 68 percent of observations fall in the first deviation, 95 percent in the second, and 99.7 percent in the third. Therefore, using this rule, one can make predictions about the final results based on the likelihood of a particular observation. In addition, this method is relatively fast and allows getting a rough estimate in cases where detailed data acquisition is impossible or costly. Finally, this law can be used to test the “normality” of the distribution (Hayes, 2021). However, since the rule of thumb is closely related to the normal distribution, it can only be applied in these cases. Accordingly, all other types of distribution, for example, skewed, are incompatible with this theory.

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In reply to one of my classmates, Jamal, I have to point out that his wording is not entirely accurate. Although my friend also notes the relationship between the rule and the standard deviation, I should note that there is nothing in the definition of the empirical rule about symmetry to a “mean.” In addition, Jamal somehow separates the three standard deviations and the normal distribution in the last paragraph of his post, as if separating them into different forms of distribution, although these parameters are closely related. Finally, a classmate of mine does not quite correctly interpret the application of the empirical rule in the context of “skew to the left” and “skew to the right.” These concepts are separate distribution laws and cannot be applied in the context of this law. Thus, Jamal’s post is not devoid of the right thoughts, but some of the wording needs clarification.

Reference

Hayes, A. (2021). Empirical rule. Investopedia. Web.

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StudyCorgi. 2022. "The Empirical Rule in Statistics." August 31, 2022. https://studycorgi.com/the-empirical-rule-in-statistics/.

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StudyCorgi. (2022) 'The Empirical Rule in Statistics'. 31 August.

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