empirical rule

(noun)

That a normal distribution has 68% of its observations within one standard deviation of the mean, 95% within two, and 99.7% within three.

Related Terms

Examples of empirical rule in the following topics:

  • Graphing the Normal Distribution

    • Each standard deviation represents a fixed percentile, and follows the empirical rule.

  • The Average and the Histogram

    • This is known as the empirical rule or the 3-sigma rule).

  • Typical Shapes

    • This is known as the empirical rule or the 3-sigma rule.

  • The Gauss Model

    • This fact is known as the 68-95-99.7 (empirical) rule, or the 3-sigma rule .

  • The Standard Normal Curve

    • From the empirical rule, we know that this value is 0.95.

  • The Normal Distribution

    • The empirical rule is a handy quick estimate of the spread of the data given the mean and standard deviation of a data set that follows normal distribution.

  • Recognizing and Using a Histogram

    • An advantage of a histogram is that it can readily display large data sets (a rule of thumb is to use a histogram when the data set consists of 100 values or more).
    • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events:

  • Lab: Probability Topics

    • The student will use theoretical and empirical methods to estimate probabilities.
    • Record the results in the "With Replacement" column of the empirical table.
    • Use the data from the "Empirical Results" table to calculate the empirical probability questions.
    • If you increased the number of times you picked 2 M&M's to 240 times, why would empirical probability values change?
    • Would this change (see (3) above) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart?

  • Lab: Continuous Distribution

    • The student will compare and contrast empirical data from a random number generator with the Uniform Distribution.
    • Construct a histogram of the empirical data.
    • Construct a histogram of the empirical data.
    • Are the empirical values (the data) in the section titled "Collect the Data" close to the corresponding theoretical values above?
    • How would that affect what you would expect the empirical data to be and the shape of its graph to look like?

  • Lab 1: Discrete Distribution (Playing Card Experiment)

    • The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a discrete distribution.
    • Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions.
    • Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions.