Empirical Rule Calculator

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How to use the empirical rule calculator?

To use the empirical rule calculator, follow these steps.

  • Enter the mean value.
  • Enter the deviation value.
  • Click "calculate"

The result will be shown in three rows consisting of 68%, 95%, and  99.7% deviation respectively. 

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The empirical rule calculator that is commonly recognized as a 68 95 99 rule calculator, is a straightforward and effective calculator that recognizes the figures of standard deviation from the mean value, either it is of 1 standard deviation or 2 standard deviations, or 3 standard deviations

In other simpler terms, it can help you determine 68, 95, and 99.7% of the data that is distributed in a graph.

We are going to discuss what empirical rule is and what its applications are and how you can use the empirical rule Calculator.


What is the empirical rule?

In arithmetic, the empirical rule states that practically any data would come inside three standard deviations of the mean in a typical set of data.

The mean value is defined as the average value of all the numbers that make a dataset. 

Empirical rule formula

The other terms that are used to call the empirical rule are the Law of 3 Sigma or the Rule of 68-95-99.7. It is because of:

  • 68 percent of all data lies inside the first standard deviation from the mean value between (μ - σ) and (μ + σ)
  • 95% of all the results would come under two standard deviations between (μ - 2σ) and (μ + 2σ)
  • Most of the results, 99.7%, comes under three standard deviations between (μ - 3σ) and (μ + 3σ) the remaining .3% is used to compensate for exceptions in almost any set of data.

How to use the Empirical rule?

Follow the steps below to understand the empirical rule.
Example:
Golf scores of a club have a standard deviation of 20 and are equally distributed with a mean of 110. Use the empirical rule to find the percentage of people scoring in a specific range.
Solution:
Step 1: Write down the values.
Mean μ = 110
Standard deviation σ = 20
Step 2: Apply the empirical rule formula:
μ - σ = 110 – 20 = 90
μ + σ = 110 + 20 = 130
68% of people scored between 90 and 130.
μ – 2σ = 110 – 2×20 = 70
μ + 2σ = 110 + 2×20 = 150
95% of people scored between 70 and 150.
μ - 3σ = 110 – 3×20 = 50
μ + 3σ = 110 + 3×20 = 170
99.7% of people scored between 50 and 170.

References :

  1. Empirical Rule explained | source by Investopedia
  2. Empirical Rule ( 68-95-99.7) & Empirical Research. Statisticshowto.com 
  3. The Empirical Rule-examples | STAT 200. PennState: Statistics Online Courses. 
  4. Wikipedia | understanding 68–95–99.7 rule 
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