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? The word with twice the frequency rank occurs (___one-fourth__OR__half__) as often.
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? The word with twice the frequency rank occurs (___one-fourth__OR__half__) as often.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.10: Inverse Variation
Problem 15P
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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.
(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?
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 (___one-fourth__OR__half__) as often.
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