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# 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 : –

1)        I selected a paragraph containing approximately 250 words from any source example newspaper etc.

2)        I read every word and obtained a frequency table for each letter of the alphabet ( table 1).

3)        I noted down the no. of two letter words, 3 letter words and so on and obtained a frequency table (table 2).

4)         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 obtain 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 foe. At this junction, all formal and in-formal agencies of education like family, school and community should realize the explosiveness of the situation. It is rightly said values can not 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 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 marvel education and character building. Intellect without wisdom can be suicidal.

Table 1

 LETTER Iftf )>/ f^ftRxS f, ■T^URr^c.y A **+*■ , «”H ^ 1-rH T-hH ; If-ft T-I-H -r7+1 H-*-/ , trH M-H ^ trr) fnij n> IV s n 1-W-l . Ui| 1 0 CL y f-H-t w-ff ^ tT+-4 . t+i-4- j-1-h- 1 > tt-H Ti M-+I rt-t 1 ; rr-H I 2- ^ r t+±i tttt j 1-1-h-l- ^ n-H , rrrl y j-rrt tt~*1 • i-f+J- ■ ttt-) f, F -t++[ H-H l-M-l Cr 1-H-! rn-> n-rt ^ o-H . j-r-H u ++-H v m-I ^ i-t-H M-H y n-tt ^ t-t+f ^ t*r+ j tn+ /-t+j- /\ i m X. t+-H , t-M-t- j rn-f , f-H-i y f-ni . rrrf y . -trt\ ^ y-ttf^ rtr\ . h-tf 105″ zr 5″ k III) ^ L_ H-h-J mW^rtrt )•«-( . .rttl rt-H rti~] j H-H no I’ll . rrri rrtf m-i y /ft) Trrt y /} f h hJ trt-i nj^rt-n y rn-f m~)^ rrtr t-rtf tr-f-i y -trrt trri^ in i o lTt-f■ y rt-t-tj rn-l / fi-M ^ tt-t-f rn~l y H-t-f «-H” MrJ >>} 9S V t++-t J IO n II 2. R f-rrt H-fi 1 J-H) rr-H r*-t-i m~/ m-i -rt-u -Mr-) 11 ^ j If j Jy ‘ X S^J ‘ ‘ M-H- ^ H-J^- i+H ^ -M-rt ++H- ^ l-H-t ^ 29 T H-I4- )+++ H-H ^l-^+f -H-f-f ^ J-if+^p ‘ )/ £ u HJ-lj M-H > -H-H- -tl )) W-H- «-H f-t+f +M4V J 1 5″7 v 7 W W-J . ) ^ x IJ 1 v -ini j j n >1 t , 17 Hi) s-
 NO-C>f WO/? DS VilTt }&JJ.V K ^ . +H4 . -H4J- -H-W- i-f-H- thfci -rH+jTH-l H O 3 ^.JL^t^LAjfi h-i^ liB^iHbjJ+^^ttH jWj^M-H ^mi t+H, ! H-+J.WI HW-,1) _ 11 H+i- j tt-H- y ttH y +J-Hf 2. O ft ^l&J^ia^o t+H- , m-h , tW~ , trH-.V+L, J; 3 2_ —1________________________________ .H+f M . 2. 2_ ++H- , ^J y tHi ^J-l-l-l 2. O c, _ J.ifc^ H-H , hH/ +Hf 7 H44 P O io Jjiip^iA ‘» ‘ ___________ 3 1 1 ^ti^ia^n. ■+++J- ) . _ 6″ 17– ” J) 11 ^a^t^o -H-H . ) 5
 S f/ Frrrrr, Wo Pds, Fr?tFQ{) e^jrv 1 /r^vo i

Investigated the following

From Table 1

(a) What is the most frequently occurring letter? Ans: E

(b)        What is the least frequently occurring letter? Ans: Q

(c)          Compare the most frequently occurring letter? Ans: A – 118, E – 136, I – 105, 0 – 98 and U – 57 E> A> I>O>U

(d)          Which vowel is least commonly used?

Ans: E (e) Which vowel is commonly used? Ans: U

(f)          Made a pie – chart of the vowels (a, e, I, o, u) and

remaining letters.

(g)          Compare the consonants in the given text.

Ans: (g)

Vowels – 43.4 % Consonants – 5.6.6%

yr C-t JlTW . /ptZQ E UHT/0oO\

, Art

 ‘COA/SOA/^N/ S

yPrrp^r c- Go- G G- HHHH VT -1 J T K K ]< v LLLLL,

Pie chart – 1

 133 1184
 x 360 = 38°

Angle of vowel A =

 141 1184
 x 360 = 42°

Angle of vowel E =

 105 1184
 x 360 = 33°

Angle of vowel I =

 98 1184
 x 360 = 30°

Angle of vowel O =

 57 1184
 x 360 = 17°

Angle of vowel U =

 930 1184
 x 360 = 200°

Angle of consonants =

From table 2

(a)      Compared the frequency of two letter words, three letter words and so on.

(b)       Made a pie chart(2) and made a interesting patterns. Ans:- (a) 2 letter – 40,

3  letter – 51,

4   letter – 17,

5  letter – 20,

6  letter – 32,

7  letter – 22,

8  letter – 20,

9  letter – 20,

10  letter – 3,

11  letter – 6,

12  letter – 4,

13  letter words – 6

Pie chart 2

 tfeClp^OCAL OF WNK Next Page

From table – 3

(a)     The relation between the frequency of a word to its rank. Ans: (a) 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. Do you see any interesting patterns?

Graph

CONCLUSION

The project given to us which was based on frequency has done a lot good to us. This has also helped us to learn how to find the frequency of letters from given text and also to plot their graph and pie chart.