Empirical Rule Calculator

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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 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.
Golf scores of a club have standard deviation of 20 and are equally distributed with mean of 110. Use the empirical rule to find the percentage of people scoring in a specific range.
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.

Normal Distribution

The empirical rule originated when analysts tended to demonstrate the same form of distribution curves again and again. 
The empirical rule refers to a regular distribution. Pretty nearly, all information in a normal distribution comes inside three standard deviations of the mean. All of them are equal in mean, mode, and median.

  • The total sum of all the figures in a set of data is the mean.

  • The mode value is indicated as the most frequent number inside the data set and it appears most often.

  • The median value is referred to the distribution within the set and lies among the highest and lowest numbers.

This implies that at the core of the datasets, the mean, mode, and median could all drop. The top end of the collection should be half of the data and the other half below.

Determining the Standard Deviation Rule

In terms of finding out the empirical rule, first, you must find the standard deviation of a given data set. By using below mentioned empirical rule formula, you can easily find the standard deviation.

empirical rule equation
 This confusing equation splits down in the following manner and here you can find out:
Evaluate the mean of a particular set of data by dividing the sum total of that dataset by the number of total figures inside the dataset. 

  • Subtract the mean for any number in the set, then square the corresponding number.
  • Assess the mean for each, using the squared values.
  • Getting the square root of the mean value is identified in the next step. 

It is the standard deviation, minus a small percentage for outliers, between the three primary percentages of the usual range from which most of the data in the package should fall.

Where is the empirical rule used?

The empirical rule is, as described above, especially useful for predicting results within a data set. 

So experimentally, a set of data could be quickly applied to the analytical rule until the standard deviation has been calculated, indicating the pieces of figures that lie in the distribution.

Forecasting is feasible and it is possible to make predictions about where information will land within the collection even without having all data information, relying on the 68 percent, 95 percent, and 99.7 percent dictates indicating where the data can settle.

In certain instances, where not all the evidence is available, the empirical rule statistics is of primary value to better evaluate findings. 

The empirical rule also seeks to evaluate how normal a collection of data is. If the data does not agree with the empirical standard, then the distribution is not natural and must be considered adequate.

In scientific analysis, the rule is commonly used, such as when measuring the probability of a given piece of data happening, or when not, all data is available, for predicting effects. 

Without any need to test all, it provides insight into the characteristics of the population and helps to evaluate when a given data set is usually distributed.

It is often used to identify outliers that could be the product of experimental mistakes-results that vary greatly from others.
Use the Empirical Rule Calculator by espacemath.com with Mean and Standard Deviation
Where espacemath.com is offering a bunch of online calculators that are helpful in solving all kinds of arithmetic problems, one of the most valuable calculators is Empirical Rule Calculator that helps in calculating the percentage of data values falling beyond a given number of standard deviation by using the mean value.

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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