The linguist George Kingsley Zipf (1902-1950) proposed a law that bears his name. In a typical English text, the most commonly occurring word is "the." We say that its frequency rank r is 1. The frequency of occurrence of "the" is about f = 7%. That is, in a typical English text, the word "the" accounts for about 7 out of 100 occurrences of words. The second most common word is "of," so it has a frequency rank of r = 2. Its frequency of occurrence is f = 3.5%. Zipf's law gives a power relationship between frequency of occurrence f, as a percentage, and frequency rank r. (Note that a higher frequency rank means a word that occurs less often.) The relationship is f = cr1, where c is a constant. (a) Use the frequency information given for "the" to determine the value of c. C = (b) The third most common English word is "and." According to Zipf's law, what is the frequency of this word in a typical English text? Round your answer to one decimal place. % (c) If one word's frequency rank is twice that of another, how do their frequencies of occurrence compare? The word with twice the frequency rank occurs ---Select- v as often.

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### Zipf's Law in Linguistics

The linguist George Kingsley Zipf (1902–1950) proposed a law that bears his name. In a typical English text, the most commonly occurring word is "the." We say that its frequency rank **r** is 1. The frequency **f** of occurrence of "the" is about **f** = 7%. That is, in a typical English text, the word "the" accounts for about 7 out of 100 occurrences of words. The second most common word is "of," so it has a frequency rank of **r** = 2. Its frequency of occurrence is **f** = 3.5%. Zipf’s law gives a power relationship between frequency of occurrence **f**, as a percentage, and frequency rank **r**. (Note that a higher frequency rank means a word that occurs less often.) The relationship is

\[ f = c r^{-1}, \]

where **c** is a constant.

**(a)** Use the frequency information given for "the" to determine the value of **c**.
\[ c = \boxed{7} \]

**(b)** The third most common English word is "and." According to Zipf’s law, what is the frequency of this word in a typical English text? Round your answer to one decimal place.
\[ \boxed{2.3} \% \]

**(c)** If one word’s frequency rank is twice that of another, how do their frequencies of occurrence compare?

The word with twice the frequency rank occurs \[ \text{---Select---} \] as often.
Transcribed Image Text:### Zipf's Law in Linguistics The linguist George Kingsley Zipf (1902–1950) proposed a law that bears his name. In a typical English text, the most commonly occurring word is "the." We say that its frequency rank **r** is 1. The frequency **f** of occurrence of "the" is about **f** = 7%. That is, in a typical English text, the word "the" accounts for about 7 out of 100 occurrences of words. The second most common word is "of," so it has a frequency rank of **r** = 2. Its frequency of occurrence is **f** = 3.5%. Zipf’s law gives a power relationship between frequency of occurrence **f**, as a percentage, and frequency rank **r**. (Note that a higher frequency rank means a word that occurs less often.) The relationship is \[ f = c r^{-1}, \] where **c** is a constant. **(a)** Use the frequency information given for "the" to determine the value of **c**. \[ c = \boxed{7} \] **(b)** The third most common English word is "and." According to Zipf’s law, what is the frequency of this word in a typical English text? Round your answer to one decimal place. \[ \boxed{2.3} \% \] **(c)** If one word’s frequency rank is twice that of another, how do their frequencies of occurrence compare? The word with twice the frequency rank occurs \[ \text{---Select---} \] as often.
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