Problème 149 – Shakespeare by the numbers

Niveau : Seconde (Classe Européenne/DNL Anglais)
Chapitres : Statistiques (en anglais)
Inédit, publié le 24/08/2020

William Shakespeare was a playwright, a poet, an actor, which is deemed by many as one of the greatest writer in the English literature – if not the greatest. « Hamlet » and « Romeo & Juliet » are probably his best-known plays, but Shakespeare’s work is much larger: called “England’s national poet”, the writer left to mankind an impressive heritage of 154 sonnets and 37 plays, which today continue to be played, studied, readapted around the world in almost all possible languages. This problem is a tribute to this extraordinary work.

The Appendix 1 includes a complete list of the 37 Shakespeare’s known plays, with their number of words. The total number of words in all plays is 835,997 words.

All results will be rounded to the closest integer.

1) Calculate the mean, the median value, the standard deviation and the range for the number of words in Shakespeare’s plays.

2) a) Fill in the Table 1 below, which classifies the number of Shakespeare’s plays by intervals of 2,000 words.

Table 1

Number of words (in thousands)	14 – 16	16 – 18	18 – 20	20 – 22	22 – 24	24 – 26	26 – 28	28 – 30	30 – 32
Number of plays

3) In Appendix 2, construct the histogram from the data in Table 1.

4) For grouped data, we define as “the modal class” the class interval that has the highest frequency number.

a) Which is the modal class of the grouped data in Table 1?

b) In general, for ungrouped data, we define as “mode” the most frequently occurring number in a sequence. There’s no mode from the list in Appendix 1 as each number appears only once. Though, for grouped data, we can define a “mode in the modal class”, which is calculated by the formula:

With the following notations:
L = lower class limit of the modal class
f₁ = frequency of the modal class
f₀ = frequency of the preceding class
f₂ = frequency of the succeeding class
H = class interval size

Calculate the mode in the modal class from the data grouped in Table 1.

Appendix 1 – List of Shakespeare’s plays ⁽¹⁾