Mathematical Calculators

Empirical Rule Calculator

The empirical rule calculator, also known as a "68 95 99 rule calculation", is a tool that allows you to determine the ranges that are either 1 or 2 standard deviations or 3 standard deviations. This calculator will show you the ranges in which 68, 95, or 99.7% of normally distributed data, respectively.

Empirical Rule Calculator

68% of data falls between
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95% of data falls between
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99.7% of data falls between
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Table of contents

What is the empirical rule?
Where is the empirical rule applied?
How does the Empirical Rule work?
What are the Benefits Of The Empirical Rule?

What is the empirical rule?

The empirical rule, also known as the three-sigma or the 68–95-99.7 rules, is a statistical rule that states that almost all data for normally distributed data will fall within three standard deviations.
You'll also find:
  • 68% data within 1 standard deviation
  • 95% data within 2 standard deviations
  • 99.7% data within 3 standard deviations
  • The standard deviation shows the spread of the data. It tells how different the data is from the average. The narrower the data range, the smaller the value.
    A normal distribution refers to a distribution that is symmetric around the mean. Data near the mean are more common than data farther from the mean. Normal distributions look like a bell-shaped curves in graphical form.

    Where is the empirical rule applied?

    This rule is used extensively in empirical research. It can be used to calculate the probability that a particular piece of data will occur or to forecast outcomes when not all data are available. It provides insight into the characteristics and distribution of a population, without having to test everyone. It can also be used to identify outliers, which are results that are significantly different from the rest of the data set. These may be due to experimental errors.

    How does the Empirical Rule work?

    The empirical rule can be used to predict probable outcomes in normal distributions. An example of this would be used by a statistician to determine the percentage that falls within each standard deviation. Consider the following: The standard deviation of 3.1 is equal to 10. The first standard deviation in this example would range from (10+3.22)= 13.2 to (10-3.22)= 6.8. The second standard deviation would be between 10 + (X 3.2 = 16.4 and 10-(X 3.2 = 3.6), and so on.

    What are the Benefits Of The Empirical Rule?

    The empirical rule works well because it is a way to forecast data. This is especially true with large datasets, and variables that are not known. This is especially true in finance. It applies to stock prices and price indices. Log values of forex rates are also relevant. They all tend towards a bell curve or normal distribution.
    John Cruz
    Article author
    John Cruz
    John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.
    Empirical Rule Calculator English
    Published: Thu Jul 21 2022
    In category Mathematical calculators
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