what is the 4σ rule of thumb in statistics
± 2 SD include approximately 95% of scores in a normal distribution. Is this what you are referring to?
The 4σ rule of thumb in statistics is a guideline often used in quality control and statistical analysis. It states that roughly 99.994% of a normally distributed data set will fall within four standard deviations (σ) of the mean.
To understand how the 4σ rule is derived, we need to know about the normal distribution, also known as the Gaussian or bell curve. In a normal distribution, the majority of the data is concentrated around the mean, with less data located further away from the mean. The spread of the data is measured by the standard deviation.
The rule of thumb is based on the empirical rule, also known as the 68-95-99.7 rule, which describes the approximate percentage of data falling within certain standard deviations of the mean in a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.
Extending this pattern, the 4σ rule suggests that approximately 99.994% of the data will fall within four standard deviations of the mean.
It's important to note that the 4σ rule is an approximation and may not hold exactly true for every dataset. However, it provides a helpful benchmark for understanding the spread of data in a normal distribution.