Chapter 5.2, Problem 10E

Reminder Round all answers to two decimal places unless otherwise indicated.

Zipf’s Law The linguist George Kingsley Zipf (1902-1930) 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 r

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?