The empirical rule formula is one of the most applied statistical methods to real-life events. For example, one of the biggest challenges manufacturing industries face is ensuring quality control and predicting possible defects. The Empirical rule immensely contributes in this area as it predicts the number of defects that may arise from an extremely large number of products through sample observation.

The rule also determines if quality control can be statistically predicted with the Vaue at Risk model(VAR), which depends on the normal distribution. This means that it can determine if the manufactured defectives from several sample sets follow a normal distribution. If, after application, it confirms that the data does not follow a normal distribution, then the VAR model cannot be a suitable method for determining the company quality control.

The empirical rule is not only useful in Quality control. It also helps predict important metrics such as disease rate in a population, poverty indexes, and other valuable metrics that could give organizations an idea of a target audience and whether it is a good investment area or not.

The bottom line is that the empirical rule uses observation to determine important information and can be applied vastly in many areas when appropriately understood.

**The Empirical rule Formula**

The Empirical Rule states that 99.7% of data lies within three standard deviations of a calculated mean as long as the data follows a normal distribution. The First standard deviations approximately cover at least 68% of the data, the second, at least 95% of the whole data, and the third, at least 99.7%.

The formula is written as;

**1**^{st}** Standard Deviation: ** (µ ± σ): (µ – σ) to (µ + σ)

**2**^{nd}** Standard Deviation: ** (µ ± 2σ): (µ – 2σ) to (µ + 2σ)

**3**^{rd}** Standard Deviation: ** (µ ± 3σ): (µ – 3σ) to (µ + 3σ)

**How to use the formula**

- Determine the Mean (µ) and Standard Deviation (σ) from the collected data
- Input the values of the µ and σ on the three formulas to get all three standard deviations
- The three standard deviations will show if the data distribution is normal. If the last standard deviation covers almost all the data, then the distribution is normal, and the formula to draw a conclusion concerning a bigger population and predict future outcomes.

**What Is the Empirical Rule?**

The term ‘empirical’ means ‘observation’ or ‘based on, which is what the rule is about. The rule provides information about a particular vast data by observing a small portion of that sample data.

The empirical rule is best used to determine a particular population’s metrics like poverty rate, the average height of thousands of a specific age group, and the cultural inclination of a specific population. The rule is also useful in calculating the expected number of defects in manufactured products.

**The role of Normal distribution in Empirical rule and Vice Versa**

- The empirical rule is dependent on the Normal distribution. The Normal distribution is symmetrical when represented graphically and shows that considered data are closer in outcomes. For example, the height of almost 18 to 20 years old males in America would be around 5.6 feet to 6.4 feet with an average of 5.9 feet. The difference between 6.4 from 5.9 feet is 0.5, while 5.9 from 5.6 is 0.3.

From the above, the average height, which is statically called the Mean (µ) is 5.9, while the lower bound of male heights is 5.6, while the upper bound is 6.4.

After subtractions, the deviations from the average height are 0.3 and 0.5, respectively.

Based on the rough sketch, it can be expected that 100 American Adults should be 5.6 to 6.4 feet with a mean of 5.9 feet. The graphical illustration of the 100 data would be symmetrical, with most of the considered heights congesting at the middle where the mean height of 5.9 is. As such, the height of American male adults can be stated to follow a normal distribution, and the empirical rule can be used to make decisions based on the information.

2.There are instances where the distribution of data may not be available, and a data analyst can figure out if it is normally distributed or not. This is especially important for manufacturing companies trying to predict the expected number of defectives. If the data is confirmed to be normally distributed by the Empirical rule, the company can use the Value at Risk Model to predict defects.So how does the company know that the data is normally distributed? The third standard deviation from the empirical rule must cover all of the data used to get the Mean or at least all of them. If most of the data is outside the lower and upper bound of the third standard deviation of the empirical rule formula, then it is not normally distributed. It also means there is a problem with the manufacturing machine(s).