# 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.

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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