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.
(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?
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