Zipf’s law is an empirical law which relates how frequently a word is used, f, to its ranking in a list of the most common words of a language, R. The law follows the form f = AR^b, where A and b are constants to be found.

The table below contains data on four words.

a. Copy and complete this table giving values of log f to 2 decimal places.

b. Plot a graph of log f against log R using the values from your table and draw in a line of best fit.

c. Use your graph to estimate the value of A to two significant figures and the value of b to one significant figure.

d. The word ‘when’ is the 57th most commonly used word in the English language. A trilogy of novels contains 455125 words. Use your values of A and b to estimate the number of times the word ‘when’ appears in the trilogy.

Transcribed Image Text:

Word Rank, R Frequency per 100 000 words, f 'the' 1 4897 'it' 10 861 'well' 100 92 'detail' 1000 9