## Standard normal distribution and the empirical rule

The empirical rule is also called the three-sigma rule, and it is known to be a statistical rule that states the normal distribution. In this distribution, all the observed values lie within the three standard deviations of the mean or average. The standard deviation is denoted by σ, and its average is denoted by µ. Specifically, the three-sigma rule predicts that 68 percent of observation lies within the first standard deviation, 95 percent are in the 2nd standard deviation, and 99.7 percent are in the 3rd one.

The manual calculation for the distribution is a complex task so, consider the empirical rule calculator to determine the normal distribution of data in the three ranges of standard deviations.

**What is the Empirical Rule?**

For the normal data set in mathematics, the empirical rule places every piece of data within the three standard deviations of the mean. On the other hand, the mean is known as the average of all numbers within the data set. Below are the reasons that why an empirical rule is referred to as the three-sigma rule:

- Sixty-eight percent of the data rests within the 1st standard deviation
- Ninety-five percent of values fall in the 2nd deviation
- Ninety-nine falls in the 3rd standard deviation.

To avoid mistakes in the calculations, use the empirical rule formula to perform the normal distribution calculations.

**Determining the Standard Deviation**

The empirical rule is important for predicting the results in data sets. For this, it is essential to determine the standard deviation. For deviation calculation, use the empirical rule formula, which is given below.

This complicated formula for empirical rule statistics breaks down in the following way:

- Calculate the mean of the data obtained by dividing the total data set by the number of numbers.
- Use the squared values to find the mean for determining the mean for each.
- Take the square root of the means calculated.

This is the standard deviation between the primary percentages of the distribution; within most of the data in the set should fall with excluding the minor percentages for outliers. You can use the empirical rule calculator to determine the standard deviation of the data set.

**Using of Empirical Rule**

The empirical rule is used specifically for the forecasting outcomes of the datasets. Once the standard deviation is calculated, the data set can easily be subjected to the empirical rule. Forecasting is possible because, despite knowing the data specification, estimates can be made regarding where the data fall within the data set. It is based on 68%, 95%, and 99% showing where the data should rest.

In some cases, it is used to determine the outcomes when the whole data is not available. It allows the statisticians to get insights into where the data will fall when all the values are available. To make things easier, try the empirical rule calculator to check the normal distribution data in three ranges of standard deviations.

**Conclusion**

In the article, we have studied facts about normal standard distribution and empirical rule. How to determine normal distribution manually with formula and empirical rule formula is also considered in this article.