Zipf's Law is an empirical rule that suggests the frequency of any word is inversely proportional to its rank in a frequency table, commonly observed in natural language and other datasets. This phenomenon implies that a few elements are extremely common while most are rare, highlighting a power-law distribution in various systems.

Zipf's Law

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical guideline that states for a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean. This rule is crucial for understanding data dispersion and making predictions about a dataset's behavior under the assumption of normality.

empirical rule

frequency of any word

rank in a frequency table

natural language

A power-law distribution is a type of probability distribution characterized by the relationship between two quantities, where one quantity varies as a power of another. It is often used to describe phenomena in complex systems, such as the distribution of wealth, earthquake magnitudes, and the frequency of words in languages, where large events are rare but significant.

power-law distribution

Common elements

Rare elements

A frequency table is a statistical tool used to organize and summarize data by displaying the number of occurrences of each distinct value or category. It provides a clear overview of the distribution of data, making it easier to identify patterns, trends, and outliers.

frequency table

datasets

A phenomenon is an observable event or occurrence that can be perceived through the senses or scientific instruments, often prompting investigation or analysis. It serves as a foundation for scientific inquiry and theoretical development, helping to explain or predict natural or social behaviors.

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