Meaning of Empirical rule formula

In Empirical rule a normal data set, virtually every piece of data will fall within three standard deviations of the mean, the mean here is the average of all the numbers within the set. The empirical rule is also known as the Three Sigma Rule or The 68-65-99 rule because of the following reasons-

  1. In the first standard deviation, 68% of all data rest.
  2. In the two standard deviations, 95% of all the data rest.
  3. In the three standard deviations, nearly all of the data i.e 99.7% rests, (the remaining 0.3% is used to account for outliers, which exist in almost every dataset)


Normal Distribution


The reason empirical rule came was that the same shape of distribution curves continued to appear over and over to statisticians. The empirical rule indicates a normal distribution. All of the data falls within three standard deviations in a normal distribution. The Mean, the mode and the median are equal.


  • The average of all of the numbers in the data set id called the mean.
  • The number that is repeated most frequently within a data set is called mean.
  • The value of the spread between the highest and the lowest numbers within the set is called the median.


This means the mean, mode and median should fall at the center of the dataset. The data should be divided into 2 parts in a data set, half should be at the higher end of the set and the other half should be at the below.


Determination of the Standard Deviation


Empirical Rule is most useful for forecasting outcomes within the data set. The first you must calculate the standard deviation. 

Here are steps of the formula

  1. The total of the data set is to be divided by the quantity of the numbers, i.e determine the mean of the data set.
  2. Subtract the mean for each number in the set, and the square the resulting number.
  3. Determine the mean for each by using the squared values.
  4. Find the Square root of the means which was calculated in step 3.

Standard deviation is between the three primary percentages of the normal distribution, in which the majority of the data in the set should fall, excluding a minor percentage for outliers.


Using Empirical Rule

The empirical rule is useful for forecasting outcomes within a data set. So once the standard deviation’s been determined, the data set can easily be subjected to the empirical rule, showing where the pieces of data lie in the distribution. 


It is possible to forecast because even without knowing all the data specifics, projections can be made as to where data will fall within the set, based on 68-95-99 i.e 68%, 95% and 99.7% dictates showing where all should rest.

 Mostly, the empirical rule is of primary use to help determine outcomes when all the data is not available. Those studying the data can gain insight into where the data will fall, once all is available. It is helpful to test how normal a data set is. If the data does not according to the empirical rule then its not a normal distribution and it should be calculated again accordingly.

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