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 = cr-1, 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? as often. The word with twice the frequency rank occu✔ -Select--- three times one fourth twice half four times Submit Answer
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 = cr-1, 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? as often. The word with twice the frequency rank occu✔ -Select--- three times one fourth twice half four times Submit Answer
Advanced Engineering Mathematics
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Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
\[ f = cr^{-1}, \]
where \( c \) is a constant.
#### Exercises:
1. **Use the frequency information given for "the" to determine the value of \( c \).**
\[
c = \_\_\_\_\_
\]
2. **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.**
\[
\_\_\_\_ \%
\]
3. **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:
- [ ] three times
- [ ] one fourth
- [ ] twice
- [ ] half
- [ ] four times
as often.
---
Submit Answer
---
In this text, there is no graph or diagram. Instead, the content focuses on understanding and applying Zipf's law to linguistic data, providing a clear mathematical relationship between word frequency and rank.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d91cf51-36b6-472d-8082-aa48d6da434d%2F71208786-7231-443b-a5a9-397b09f8c1e3%2Fszg8cj9_processed.png&w=3840&q=75)
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
\[ f = cr^{-1}, \]
where \( c \) is a constant.
#### Exercises:
1. **Use the frequency information given for "the" to determine the value of \( c \).**
\[
c = \_\_\_\_\_
\]
2. **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.**
\[
\_\_\_\_ \%
\]
3. **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:
- [ ] three times
- [ ] one fourth
- [ ] twice
- [ ] half
- [ ] four times
as often.
---
Submit Answer
---
In this text, there is no graph or diagram. Instead, the content focuses on understanding and applying Zipf's law to linguistic data, providing a clear mathematical relationship between word frequency and rank.
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