Maths Project on Frequency of letters or words in a Language
Frequency of Letters or Words in a Language
Objective:
Analysis of a language text, using graphical and pie chart techniques.
Description:
- I selected a paragraph containing approximately 250 words from any source (example: newspaper, etc.).
- I read every word and obtained a frequency table for each letter of the alphabet (Table 1).
- I noted down the number of two-letter words, three-letter words and so on, and obtained a frequency table (Table 2).
- I selected 10 different words from the text which had frequency greater than 1. Gave ranks 1, 2, 3 … 10 in decreasing order of their frequency and obtained Table 3.
The Paragraph
EROSION OF ESSENTIAL VALUES AND THE NEED OF OVERHAULING EDUCATION SYSTEM
Education is a sub-system of the wider social system. Although it functions autonomously, it has linkage with the economic, political, religious and other sub-systems which enter a powerful influence on the goals of the educational sub-systems.
Due to globalization and modernization, our society is passing through momentous changes in its value system. Values of yesteryears have taken a back seat and materialism, corruption and dishonesty and other negative values have come to the fore. At this junction, all formal and informal agencies of education like family, school and community should realize the explosiveness of the situation. It is rightly said values cannot be taught, they are caught.
All the agencies should become role models if we want our youth to be on the right path. Absence of a congenial and loving atmosphere and quarrel among parents are the major hurdles in this direction. Race for degrees and jobs has deteriorated the situation. On the other hand, formal education is squeezed between memory and mechanisation.
The whole system of education needs complete overhauling. If at all we the citizens are desirous of thwarting deterioration in values, teaching at all levels must emphasize a moral education and character building. Intellect without wisdom can be suicidal.
Table 1 - Frequency of Each Letter
| Letter | Frequency Count | Frequency |
|---|---|---|
| A | (tally) | 118 |
| B | (tally) | 10 |
| C | (tally) | - |
| D | (tally) | 24 |
| E | (tally) | 136 |
| F | (tally) | - |
| G | (tally) | - |
| H | (tally) | 30 |
| I | (tally) | 105 |
| J | (tally) | 5 |
| K | (tally) | 4 |
| L | (tally) | - |
| M | (tally) | - |
| N | (tally) | - |
| O | (tally) | 98 |
| P | (tally) | 10 |
| Q | (tally) | 2 |
| R | (tally) | - |
| S | (tally) | 29 |
| T | (tally) | 115 |
| U | (tally) | 57 |
| V | (tally) | 7 |
| W | (tally) | 4 |
| X | (tally) | - |
| Y | (tally) | 17 |
| Z | (tally) | 5 |
Table 2 - Frequency of Words by Length
| Number of Letters in Word | Frequency |
|---|---|
| 2 | 40 |
| 3 | 51 |
| 4 | 17 |
| 5 | 20 |
| 6 | 32 |
| 7 | 22 |
| 8 | 20 |
| 9 | 20 |
| 10 | 3 |
| 11 | 6 |
| 12 | 4 |
| 13 | 6 |
Table 3 - Top 10 Words by Frequency (with Rank)
| Rank | Word | Frequency |
|---|---|---|
| 1 | - | 1 |
| 2 | - | 4 |
| 3 | - | 3 |
| 4 | - | 8 |
| 5 | - | 5 |
| 6 | - | 6 |
| 7 | - | 7 |
| 8 | - | 5 |
| 9 | - | 9 |
| 10 | - | 10 |
Investigations
From Table 1
(a) What is the most frequently occurring letter? Ans: E
(b) What is the least frequently occurring letter? Ans: Q
© Compare the most frequently occurring vowels. Ans: A - 118, E - 136, I - 105, O - 98, U - 57. Order: E > A > I > O > U
(d) Which vowel is least commonly used? Ans: U
(e) Which vowel is most commonly used? Ans: E
(f) Pie chart of vowels (A, E, I, O, U) and remaining letters:
Angle calculations for Pie Chart 1 (Total letters = 1184):
- Angle of vowel A = (133 / 1184) x 360 = 38°
- Angle of vowel E = (141 / 1184) x 360 = 42°
- Angle of vowel I = (105 / 1184) x 360 = 33°
- Angle of vowel O = (98 / 1184) x 360 = 30°
- Angle of vowel U = (57 / 1184) x 360 = 17°
- Angle of consonants = (930 / 1184) x 360 = 200°
Graph: Pie chart showing the proportion of each vowel (A, E, I, O, U) and consonants as sectors, plotted from the angle values above.
(g) Compare the consonants in the given text. Ans: Vowels - 43.4%, Consonants - 56.6%
From Table 2
(a) Compared the frequency of two-letter words, three-letter words, and so on.
Ans:
- 2-letter words: 40
- 3-letter words: 51
- 4-letter words: 17
- 5-letter words: 20
- 6-letter words: 32
- 7-letter words: 22
- 8-letter words: 20
- 9-letter words: 20
- 10-letter words: 3
- 11-letter words: 6
- 12-letter words: 4
- 13-letter words: 6
(b) Made a pie chart (Pie Chart 2) and observed interesting patterns.
Graph: Pie chart showing the distribution of word lengths (2-letter through 13-letter words) as sectors, plotted from the frequency data in Table 2 above.
From Table 3
(a) What is the relation between the frequency of a word and its rank? Ans: Higher the rank of a word, higher is its frequency.
(b) Plot a graph between the frequency and reciprocal of word rank. What do you observe?
Graph: Graph of frequency vs. reciprocal of word rank, showing the relationship between word rank and frequency (plotted from data in Table 3 above).
Conclusion
The project given to us, which was based on frequency, has been of great benefit. This has helped us learn how to find the frequency of letters from a given text and also to plot their graph and pie chart.