Formula of Empirical Rule
Empirical Rule Formula is as follows:
One Standard Deviation (µ ± σ): 68% of Data
Two Standard Deviation (µ ± 2σ): 95% of Data
Three Standard Deviation (µ ± 3σ): 99.7% of Data
- About 68% of data falls within one standard deviation of mean.
- Approximately 95% of data falls within two standard deviations of mean.
- Nearly 99.7% of data falls within three standard deviations of mean.
This rule applies to data that follows a normal distribution, represented by a bell-shaped curve. It provides a guideline for understanding the distribution of data points around the mean. The Empirical Rule is useful for analyzing and interpreting data, helping to identify trends, outliers, and patterns in datasets.
For Example: Suppose we have a dataset representing heights of students in a class, and data follows a normal distribution with a mean height of 65 inches and a standard deviation of 3 inches.
About 68% of students’ heights fall within one standard deviation of the mean. Using Empirical Rule, we can calculate that the range of heights within one standard deviation of mean is from 62 inches to 68 inches (65 ± 3). So, approximately 68% of the students have heights between 62 inches and 68 inches.
Approximately 95% of students’ heights fall within two standard deviations of the mean. With a standard deviation of 3 inches, the range within two standard deviations of the mean is from 59 inches to 71 inches (65 ± 2 × 3). Therefore, nearly 95% of the students have heights between 59 inches and 71 inches.
Nearly 99.7% of students’ heights fall within three standard deviations of the mean. The range within three standard deviations of the mean is from 56 inches to 74 inches (65 ± 3 × 3). Hence, almost all students, about 99.7%, have heights between 56 inches and 74 inches.
Empirical Rule
Empirical Rule, also known as the 68-95-99.7 rule, states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this article we will understand, Empirical Rule, Normal Distribution, Standard Deviation, Applications of Empirical Rule, Empirical Rule Formula, and others in detail.
Table of Content
- What is Empirical Rule?
- Normal Distribution
- Empirical Rule and Standard Deviation
- How Does Empirical Rule Work?
- Formula of Empirical Rule
- Empirical Rule Vs Chebyshev’s Theorem
- Chebyshev’s Theorem
- Applications of Empirical Rule