Zipf's law facts for kids

Zipf's law is a cool idea about how often words appear in a language. It was created by a smart linguist named George Kingsley Zipf. He used math and statistics to figure it out.

Zipf's law says that if you look at a lot of words, the most common word will show up about twice as often as the second most common word. It will show up three times as often as the third most common word, and so on. So, if a word is ranked number n in how often it appears, its frequency is like 1 divided by n (1/n).

For example, in English, the word "the" is usually the most common. It makes up almost 7% of all words! The second most common word, "of," shows up about 3.5% of the time. Then comes "and." This pattern means you only need about 135 words to make up half of all the words in a big text.

Beyond Words: Where Else Does Zipf's Law Appear?

This interesting pattern isn't just for words! It shows up in many other things too. For example:

• The populations of cities in different countries.
• The sizes of big companies.
• How much money people earn.

A scientist named Felix Auerbach first noticed this pattern in city populations way back in 1913. It's still a bit of a mystery why Zipf's law works for so many different things, including most languages.

Images for kids

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  A graph showing how often words appear in 30 different Wikipedias. The most common words are on the left, and less common words are on the right.

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  This graph shows how often words appear in Wikipedia. The word's rank (how common it is) is on the bottom, and how many times it appears is on the side. The most popular words are "the," "of," and "and." The green line shows where Zipf's law fits best.

See also

In Spanish: Ley de Zipf para niños