Empirical or 68-95-99.7 Rule Calculation
Empirical Rule in Statistics
Empirical Rule, also known as the 68-95-99.7 rule or three-sigma rule, is a statistical concept used to describe how data is distributed in a normal distribution. It states that 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviations from the mean, and 99.7% of the data lies within three standard deviations from the mean.
Understanding Normal Distribution
To understand the empirical rule, it's important to first understand the concept of normal distribution. Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric around the mean. In a normal distribution, the mean, median, and mode are all the same value.
The normal distribution is often used in statistical analysis because many natural phenomena follow this pattern. For example, the height of people in a population is often distributed normally, with most people being close to the average height, and fewer people being much taller or much shorter.
Standard Deviation
Standard deviation is a measure of how spread out the data is in a dataset. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
A small standard deviation indicates that the data is clustered around the mean, while a large standard deviation indicates that the data is more spread out. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
Applying Empirical Rule
The empirical rule is a useful tool for understanding how data is distributed in a normal distribution. For example, if we know that the heights of a group of people are normally distributed with a mean of 5'6" and a standard deviation of 2 inches, we can use the empirical rule to estimate the percentage of people in the group who are between certain heights.
Approximately 68% of people in the group will have a height between 5'4" and 5'8", approximately 95% will have a height between 5'2" and 5'10", and approximately 99.7% will have a height between 5'0" and 6'0".
Conclusion
In conclusion, the empirical rule is a useful concept in statistics that describes how data is distributed in a normal distribution. By understanding the empirical rule, we can estimate the percentage of data that falls within certain ranges, and make predictions about future data based on past trends.
Mermaid Diagram
mermaidCopy code
pie
title Distribution of Data
"Within One Standard Deviation": 68
"Within Two Standard Deviations": 27
"Within Three Standard Deviations": 5
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