Topic: Methods of Data collection-Primary and secondary Data

There are two types of data: 1. Primary Data and 2. Secondary Data
1. Primary Data: It is a term for data collected at source. This type of information is
obtained directly from first hand sources by means of surveys, observations and
experimentation and not subjected to any processing or manipulation and also called primary
data. Primary data means original data that has been collected specially for the purpose in
mind.It means someone collected the data from the original source first hand.

Primary data has not been published yet and is more reliable, authentic and objective. For
example population census conducted by the government of India after every 10 years.

2. Secondary data: It refers to the data collected by someone other than the user i.e. the
data is already available and analysed by someone else. Common sources of secondary data
include various published or unpublished data, books, magazines, newspaper, trade journals
etc.

COLLECTION OF PRIMARY DATA

Primary data is collected in the course of doing experimental or descriptive research by
doing experiments, performing surveys or by observation or direct communication with
respondents. Several methods for collecting primary data are given below-
1. Observation Method
It is commonly used in studies relating to behavioural science. Under this method
observation becomes scientific tool and the method of data collection for the researcher, when
it serves a formulated research purpose and is systematically planned and subjected to checks
and controls.

(a) Structured (descriptive) and unstructured (exploratory) observation- When a

observation is characterized by careful definition of units to be observed, style of observer,
conditions of or observation and selection of pertinent data of observation it is a structured
observation. When there characteristics are not thought of in advance or not present. it is a
unstructured observation.

(b) Participant, Non-participant and disguised observation- When the observer observes by
making himself more or less, the member of the group he is observing, it is participant
observation but when the observer observes by detaching himself from the group under
observation it is non participant observation. If the observer observes in such manner that his
presence is unknown to the people he is observing it is disguised observation.

(c) Controlled (laboratory) and uncontrolled(exploratory) observation- If the observation

takes place in the natural setting it is a uncontrolled observation but when observation takes
place according to some pre-arranged plans ,involving experimental procedure it is a controlled
observation.

Advantages-
• Subjective bias is eliminated.
• Data is not affected by past behaviour or future intentions.
• Natural behaviour of the group can be recorded.
Limitations-
• Expensive methodology.
• Information provided is limited.
• Unforeseen factors may interfere with the observational task

2. INTERVIEW METHOD
This method of collecting data involves presentation of oral verbal stimuli and deeply in
terms of oral- verbal responses. It can be achieved by two ways:-
(A)Personal interview- It requires a person known as interviewer to ask questions generally
in a face to face contact to the other person. It can be –
Direct personal investigation- The interviewer has to collect the information personally
from the services concerned.

Indirect oral examination- The interviewer has to cross examine other persons who are
suppose to have a knowledge about the problem.

Structured interviews- Interviews involving the use of pre-determined questions and of

highly standard techniques of recording

Unstructured interviews- It does not follow a system of pre-determined questions and is

characteirzsed by flexibility of approach to questioning.
Focussed interview- It is meant to focus attention on the given experience of the respondent
and its effect. The interviewer may ask questions in any manner or sequence with the aim
to explore reasons and motives of the respondent.

Clinical interviews- It is concerned with broad underlying feeling and motives or

individuals life experience which are used as method to collect information under this
method at the interviewer direction.

Non directive interview- The interviewer`s function is to encourage the respendent to talk
about the given topic with a bare minimum of direct questioning.

Advantages-
• More information and in depth can be obtained.
• Samples can be controlled.
• There is greater flexibility under this method
• Personal information can as well be obtained.
• Mis-interpretation can be avoided by unstructured interview.
Limitations
• It is an expensive method.
• More time consuming.
• Possibility of imaginary info and less frank responses.
• High skilled interviewer is required
(B) Telephonic interviews- It requires the interviewer to collect information by contacting
respondents on telephone and asking questions or opinions orally.
2. QUESTIONNAIRE
In this method a ouestionnaire is sent (mailed) to the concerned respondents who are
expected to read, understand and reply on their own and return the questionnaire. It consists
of a number of questions printed or typed in a definite order on a form or set of forms.
It is advisable to conduct a ‘pilot study’ which is the rehearsal of the main survey by experts
for testing the questionnaire for weaknesses of the questions and techniques used.

Essential of a good questionnaire

It should be short and simple.
• Questions should processed in a logical sequence.
• Technical terms and vauge expressions must be avoided.
 • Control questions to check the reliability of the respondent must be present.
• Adequate space for answers must be provided.
• Brief directions with regard to filling up of questionnaire must be provided.
• The physical appearances-quality of paper, colour etc must be good to attract the
attention of the respondent
Advantages
• Free from bias of interviewer.
• Respondents have adequate time to give answers
• Respondents are easily and conveniently approachable Large samples can be used
to be more reliable.

LIMITATIONS
• Low rate of return of duly filled questionnaire.
• Control over questions is lost once it is sent.
• It is inflexible once it is sent.
• Possiblitty of ambiguous omission of replies.
• Time taking and slow process.
3. SCHEDULES
This method of data collection is similar to questionnaire method with difference that
schedule are being filled by the enumerations specially appointed for the purpose.
Enumerations explain the aims and objects of the investigation and may remove any
misunderstanding and help the respondents to record answer. Enumerations should be well
trained to perform their job,he/she should be honest hardworking and patient. This type of
data is helpful in extensive enquiries however it is very expensive.

Collection of secondary data

A researcher can obtain secondary data from various sources.Secondary data may either be
published data or unpublished data.

Published data are available in:

a. Publications of government.
b. Technical and trade journals.
c. Reports of various businesses, banks etc.
d. Public records.

e. Stastistical or historical documents.

Unpublished data may be found in letters, diaries, unpublished biographies or work.

Before using secondary data it must be checked for the following characteristics-
1. Reliability of data- Who collected the data? From what source? Which method? Time?
Possibility of bias? Accuracy?

2. Suitability of data- The object scope and nature of the original enquiry must be studies
and then carefully scrutinize the data for suitability.

3. Adequency- The data is considered inadequate if the level of accuracy achieved in data
is found inadequate or if they are related to an area which may be either narrower or
wider than the area of the present enquiry.
 ion ano
. Collect. f Da ta
Representation o

data. speci fic apec ts of statls u~ ·

aryand secon dary
of dllta : PrbD • Wha t is the n~ of ~&ssiflcat;"'1l
colfedla'I Stali.<d""' unllS• •ng Of ciassiflcatJO O. • tion. Class ifiaat ion acc l'dii,
.Mearu r dassi fica C 0 I
data. iction
. of data : jficatiO . D· -rupes
.., o• to c•~ - inter vals. • onstn u
"I
QasdficatiOD
Objectives of cJd ificati oit acconUng ,Hi:tr ibutio n, Con tinu o• fr-equtllty
t Cid
I
fi uency ~ agnit udes.
.
to attrlbu es. . Discre te req
distrib ution - d their DI
tabul ation . Rules o•'l
frequency .
be
Num r
of cla§e s ans·
f tabula tion. ig ni ti,cance of •
distribution. .
. of data : Need o
Tabula tion
tabula
.
tion,
~ .. ,.,_,
of tables ""' of grap hs. Meth ods of prep
. arati on of
frequency
ntatio n of data : ., pes on. Frequency . curv e. Rela bve "fi
•
Graphic prese polyg s·
. e
ency curve or og1v • Dot diagr am. •gm •cance of
grapuL . Histo gram. Frequ
map Cumulative frequeLimitncy . f graph ic prese ntati on.
. · ations o
grapl, ic repres entat, ~n. . Line diagram. Bar diag ram. Pie diagrlllll.
Diagr amma tic representation of data . .
Exercise.

Collection of Dat a

The study of techniques of collection of data and its presentation

enables one
to draw reliable conclusions from the collected data, which is obta
ined through
various experiments ·and helps in analysis and interpretation.
Primary and secondary data
)ata obtained by an · · ~ .
t>rimary rnve
data stiga
Wbe tor 1
ifor
d the first
. time are original one and are
ailed ~
~C-33) · reas ata are collected by some other persons
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]) 1b ,nokc 11c uno : • ro '"" unpor ,·"1~
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(4) '' al ro sua us
our unnecessaryoUec ted anotcrb
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ur up tfio c finnl roport .

I d11 1ftin g of c~1~ f the raw dutn and rnnkc it possible IO Ur
(5) To p d1<'
(6) To he P ploxaues O Q~
. pli fy the com
(7) To s1m
dat a.
statistical inforon cc's. f the coUc,cted
~r us e o
To ma ke pr or
(8)
d o n . . d out dep end s on the. ryp.cs.. of.dar n bc,h.
Tv nM ol ~ .
•1 r- . . to be carno et rwo typ es of cla ssat 1ca11on _ R
The typ e of cJa ssa fica uon me
II
b. tatistics we usua y te and
dealt .with. In . ios rdi to attribu
Cla ssd ica aon acco .ng to ·class interva1s.·
(I) . .
acc ord ing i t att rib ute s. Various enquiries deal W11h.
(2) Classificauon O . . .
__:n don accord ngd t quanu•tauve characlenst1cs and also 11nttli
.
....-.ca .
,.

1. CJ . .
hi h can be reduce too quantitative charactcnslJcs. In this c .
phenomena w c red ed . . asc
which cannot rd. uct the attribute that a particular phenomcn on
be
th ose . . di h.
upi ng is don e acco ange/foem aJe int elh gen t/d ull , re w 1te etc . Such a
·gro --• ' . .b .
ess es. For exa mp 1e, uaaa aur a ute s. llu s may bc
poss . . . k , classification according to
classdicatJon 1s nown as · .
.
simple or :manifold. ect of cla ss1 fica t1o n ca_n_be pui under
(a) Simple classificalion. Here the obj two
population may be class1f1ed into
two columns. For example, human e,
as ma Jes and fem ale s, ma rrie d and unmarried, literate and illiterat
categories
.
rich and poor etc . classification in which more lhan one
(b) Ma ai/o ld cla ssif ica tion . It is the
le, we
For a fish population, for an examp
attribute is studied simultaneously.
ide the pop ula tion into ma le ~nd female on the basis of the
may first div healthy
ibu te "se x". Eac h of the se cla sse s may be further subdivided into (I
attr
the bas is of attr ibu te "he alth ". Th e subdivision may further be
and diseased on
tes.
divided on the basis of other attribu of
(
ss interval. When classification
2. Classification according to cla
is don e acc ord ing · to som e measurable quantity, such a
obse~ati~ns .
15 known as quantitative classification
or numerical classification
classif ica tion
st ri'b utio n. In this typ e of cla ssi fication direct quantitative
or frequency di
Colltrcrion o"'I lfrp rr.m lfatio11 of Data [ 2/

measurement of <l ~ta is possibl e. Every frequency distribution possesses two

charnctcri sties- .
( I) The data arc simultaneously collected at a point in time so that the time
element is not variable.
(2) The classification is made according to the magnitude of the variable rather
than its quantitative or geographical characteristics .
Constniction of frequency distribution
If there are repetitions in individual values or items of investigation suitable
frequency table can be framed . These frequency tables may be discrete or
continuous in nature, out they must maintain the frequency concerned in their
respective classes .
Discrete frequency distribution. All the observations are listed in
ascending or descending orders.
Following raw data were obtained in a biological experiment. Rate of
reproduction (Fecundity) of 50 fishes was recorded as follows -
Raw Data (A)
80 70 70 70 16 50 20 20 20
45 16 50 30 65 40 30 50 so
70 45 20 70 2 79 16 20 19
40 50 30 2 45 30 50 45 30
40 45 80 50 39
50 50 20 30
A frequency distribution table is framed on the basis of above raw data.
Following steps are taken while framing frequency distribution table.
Conve rting raw data in arraye d data. The primary duty of a
biostatistician is to convert raw data in arrayed data. This can be done by
arranging the raw data into ascending or descending orders. For biostatistics
data are usually arranged in an ascending order. The above raw data arranged
in ascending order to make arrayed data
Arrayed Data (8)
2 2 2 16 16 16 16 20 20 20 20 20 20 20 30
30 30 30 30 30 30 30 40 40 40 45 45 45 45 45
45 50 50 50 50 50 50 50 50 50 65 65 70 . 70 70
70 70 80 80
Framing a simple frequency table (grouped series in discrete condition) :
( 1) A table of two columns is framed. First column contains variables and
second column contains repetition number i.e. frequency of variables.
(2) On persual of the above arrayed data (B), we find that variable 2 is
obtained thrice. Therefore, frequency 3 is mentioned in second column i.e.
in the frequency column. Variable 16 is obtained four times and hence 4
f zz J ,.. the sa111'-' -- distribution table is ·•• 'v ' ll -
. ed f cqu fra ati.~b\ '
is JJlenuon dfollowing r encY
v•
l'llc<1 ~\
~ \
111eotio ned an '
30
45
5
49
I
50
9
6S ,o
2 16 2 S 1~
7 1
".,.. ..,., 4 7 I ~.
.....r_y 3 ·bution table. Wh en the
•
'l
,re q.- - d1s tn
ontinuoUS . ete frequency d.tstn.butio t\\lt...
. g a c the d1s cr n con ••1bt1
Ff11111'n f'\/ \arge, data in some pre determined S\lll\
bse rvat
.
tons
are ve, ; up the "ti .
. t ~~:.
. So we gro
0
· is kn°W n as .clas•s1 icat,on accord·intelvq\~\
of space and ume-\ass •
s distnbutton. Th· e classif. icaing
S ch a c ificauon nun .
uou f
t Ii.
.\} ~,.
groups. u d rep resents the co s the fol
. lon
lowing three basic p (}f d'~
intervals an .h c1ass interva15· 1·nvo1ve and . rob\ ,
ording to t e , \,er of classes their magni tudes. t~
ace . . the nur n . • .
( 1). 0eterrn1 ning
. the appropna . te cla ss hnu ts.
(2) choosing in each class.
unt ing the nur nbe r h . magnitude. In a continu .
(3) Co and t e1r ous fre
ber of classes b .
Num be of clas ses
.
i
nto wh ich the o servations are quc~ d.. ~
.,
distn"bution • the nurn r le Toe 1arge r the number of observatio .
ns rn
1~1d.
~
a very important ro · th . . • ore
1
p ays mb er of classes m a continuous fren "'1 i t.

.the number of classes. Though de nut· be

. . ti ed it too many or too less. An ideal-'tile~ nu
~
distribuuon 1s not ix • sbo ul no
· y freq d" stribution would be th at which .
gi\ie
ll\titi
of classes for man . uen cy i . s ,~.
. . f ation m the c1eare st fas hio n. In practice, we usually tak~I'(
maximum m orrn d .rnurn of 20 classes. e\
minimum of 3 an. maxi al . ·an invest
•r he highest v ue m igation be 76 and the smallest va\
Thu s, 1 t db _= .
3, the difference woul e 76 3 73 _ Suppose, we would hke to di'Jide l\\t
Ut
. . then the class number wou ld be 73/ 10
infonnat1on mto 10 c1asses, =7.3.
.
Number of classes can be dec ide d with the help of Sturge rule. This. ru\e
tells that the number of classes would be
-
. k = 1 + 3.322 log N
Where, N = Total number of observations.
log = logarithm of the number
For example, if 100 observations are bei
ng made, the number of c\asse~
will be :
k =l + (3.322 x 2) =1+ 6:644 = 7 .64
4 or 8.
Classification of arrayed data into con
tinuous frequency distribution.
Values of variable are kept into ordered
class intervals. The width or •range ol
class is called class interval. The width
of class intervals is kept at a uniform
size and is denoted by i.
Size of class interval depends on the
range of da ta and the number oi
classes. The range is the difference betwe
en the highest and lowest value of the
 I 23
Collection and Rcpresentatio,r of Data
·fr e between the
· blc The class interval would be equal to the d1 erenc
van a . · . . be 0 f classes.
highest and the lowest values of the variah!e d1v1ded by th~ num ~
The following fonnula may be used to estimate the class interval ·
. H-L
1= - -
K
where, ; = width of class interval : H = highest value of variable
L = lowest value of variable k = the number of classes.
To illustrate the construction of a frequency distribution table in class
interval, let us consider the arrayed data (B) which represents the rate of
reproduction in SO fishes of a species.
First of all we have to find out the number of classes.
According to sturge rule k = l + 3.322 log N.
Here, k = l + (3.322 x l) = 1 + 3.322 = 4.322 or 5.
Therefore, the .mumber of classes may- be 5. ,
After deciding the number of classes, we should find out the suitable width .
of class interval.
. al
1 mterv or l
Cass =x
. H-L

See arrayed data (B). It shows the highest value of observation is 80•ancl
lowest value is 2 and number of classes i.e. k is 5.
i =80 - 2 . = 78 = 15
5 5
Thus, a table may be framed having width of class interval 10 or 15. But
for convenience, an investigator can take suitable number of classes and width
of class interval. Frequency distribution table in class interval may be prepared
iii two ways :
(a) Overlapping frequency table or exclusive method. Values of v·ariables
are grouped in such a fashion that the upper limit of one class interval is the
lower limit of succeeding class interval. An overlapping class interval
frequency distribution table can be prepared using data of Table 4.1.
Data of table 4.1 tells that the rate of rep009uction of the given species of
fish ranges between 2 and 80. W,.e can keep the width of class interval 10. Then
the range of first class interval will be 0-10, 2nd between 10-20, 3rd between
20 -30 and so on. Here one thing is remarkable - fishes having rate of
reproduction upto 9 are taken into consideration in the first class interval. On
persual of table 4.1, it appears that 3 fishes come under this class interval.
Therefore, the frequency of class interval 0-10 is 3. Fishes having 10 rate of
reproduction have to be included in the succeeding class interval. Four fishes
come under second class interval. Hence, frequency of 2nd class interval is 4
(Table 4.2).
 . s~ .....-- ·
(bJ '~e grou~ cceeding cia of table 4.1. - · -"<lPPtng ft --,~,,
tq'1t \
vsirisi,leSverlaP tbe sduusing the dal~ 10, 11 - 20, 21 - 30
ot O
and s ~\ ,
do 11 r,e prepare val tnaY be · · f
upper hm1t o one clas . ~~.
O0
t\ t
3 call s inter I-Iere . s in~ 111~
4. r1ere cla5 . tef'lal 10· eding
1 ss .1n clas s interval (Table
n
·dth of c a 1 wer lirntt
. of prece 4.3) Iv~ .\\
~
Wl d by 0 Tabk 4.3 . '
0
verlaPpe
'(llblt 4.z table Non-overlapping fre
rre'luencY Cllltllq
o"ertaPPinl Class lnte nal F
'-~t
frequeOCY _ _i- --- -:- ::- -- - "q~
1
Cla§ 1nterl'• 1 - 10
3
O _ 10 11 - 20
4
10 - 20
7 21 - 30
20 - 30 31 - 40
8
30 - 40 4
9 41 - 50
40 - 50 15
9 51 - 60
50 - 60 0
2 61 - 70
60 - 70 7 \

6 71 - 80 I
70 - 80 3
2 81 - 90
80 - 90 0
IJ=50 II =so
. atts
Note _ For b1ost • u·cs usually non-overlapping frequency distribution
· table is Used
·
Preparation . of . cumulative frequency c&tribution
table,
relative cumulative frequency table and
% cumulative frequency table
Following steps have to be taken to frame cumulative freq
uency table, relative
cumulative hequency table and % cumulative frequency
table -
A table of five columns is framed. In frrst column
class interval is ~ven.
In 2nd column frequency is noted. In 3rd column
cumulative frequent, are
mentioned. (For the preparation of cumulative· frequen
cy distribution, add
frequency of first class interval with the frequency of 2nd
class interva\. Say
~e frequency of first class interval is 3, then the freq
interval is noted as 3 Th fr
uency of first c\ass
. . .
· e equency of second class inte
witb 3. Total comes to 14 Thi rval 1s 11 then au.id \\
· val. Now · s 14 · 2 d lass
inter if the fre . 1s cumulative frequency of n c ,
comes to 2l F quency of 3rd class interval is 7 then add 14 and 7·This
fashion cu~ ul: ~:: Y of 3rd class interval is mentionC!l
as 21. In the saine
column is for - ·ti equency of each class .interval is
1a ve CUinul ti ascertained). Fou~
a v.e frequency. (For preparation f re\auve
&~

°
Tabulatiota "' Data
Tabulation is a pr f
, occss o ordeTly arrangement of data . .
co ) umns where the be . . mto senes of
e asily understooo ~ n read J~ two dunensions. Tabulated data cai:ow\ ' tw.i
makes the summati t .o se which are not tabulated. A tabular arr he ll\()f\
on o Items and detection of errors and om.i . iln&ctncl\t
Need or tabulation ss1ons Cclsicr.
Statistical tabulation is
one of the simpl t d
for summarising data in es an most revealing devices Ill
an orderly manne . ~\
features and chief characten .; r so as to bnng out its essent· \
Sues A t bl . . la
statistical data in columns and r · · a e is a systematJc arrangement ()f
. ows. Tables mak 1.t "bl f
present a huge mass of data in a d . e poss1 e or the analyst to
etai\ed orderly ·thi th · .
space. Tabular presentation of raw da . manner w1 n e mtrumurn
reporting . ta 18 the cornerstone of statistica\

Significance of ta~ulation
It simplifies complex raw data It facilitates com . be . .
. . . panson tween different
values of a parameter. It gives 1denuty to the data. It reveal tte .thi
s pa ms w1 n the
figures . It facilitates the detection of errors and omissions.

Rules of tabulation
There is no hard and fast rule for _tabulation of data because much depends
upon the given data and requirement of the ·survey. However, following general
considerations may be kept in view w~e tabulating data -
( l) The table should suit the size of the paper usually with more rows than
columns. It is des~able to make a rough draft of the table before the
figures are entered into it
(2) ln an tables; number, heading and sub-beading should be arranged in some
systematic order such as alphabetical, chronological, attributes etc .
O) The points of measurement should be clearly defined and given in the tab\e
such as \ength •
(4) f · m cm or weight in g etc.
'i,Ures shou\d b
a t~. e rounded off to avoid unnecessarv details in the tab\e and
"""note \.o th. "
(S) lbe \ab\ ts effect should be ·given
h c should not b .
s ()utu be ~re e o verloaded with details rather a number of tables
\)ar, ic pared . E ach b ,
U\ar {)\itp()'-e. - ta \e should be complete 1n itself and serve a
 ,. ( pata t of data jnto series of rows
0
TabuJ11tion of orderly arrangeme:ions. Tabulated data. can be rnar.;i or~
. a process . two dimen arran ge,n
T1bul1tion ,s . can be read h.in h arc not tabulated. A
tabu lar
·. t,ere theY . . . erit
. 0 of errors and om1 sswn s easie r
coJ,umns w od thaJ1 (hose w '' .
e3SilY unJersw .. of items and detecUO
makes the surrunauon
__., of uabOladon . Jest and most revealing devices meant
N~ . ne of the s1ll1P b. t .
d ly man ner so as to nng ou its essential
iscicaJ r.abtdation is o ·
Stat · an or er
for summarising data in . . A table is a systematic arrangement of
h . f haractensucs. Tables make it. poss1'bl e fior the analyst to
features and c ie c . .mum
. . lumns and rows.•l'.l•Jed orderly manner w1·tru·. n the rruru
statisucaJ data in co . . d
of data mfa euu w data is the cornerstone of statistical
present a huge mass .
Tabular presentation o ra
'
space. .
reporting.
ifkance of tabulation data It facilitates compans .
S'gn
1 . - on between different
.
. . I . .
It s1mphfies comp1ex raw ident ity to the data It. reve a s patterns within the
arameter. It gives .
vaJ ues o f a p .
figures. It facilitates the detection of errors and orruss1ons.

Rults of tabulation use much depends

There is no hard and fast rule for .tabulation of data beca
upon the given data and requirement of the ·survey. However
, following general
considerations may be kept in view whi!e tabulating data -
more rows than
(I) The table should suit the size of the paper usually with
before the
columns. It is des;able to make a rough drait of the table
figures are entered into it
(2) In all tables; number, heading and sub-heading should be
arranged in some
systematic order such as alphabetical, chronological, attribute
s etc.
(3) The points of measurement should be clearly defined
and given in ·the table
such as length in cm or weight in g etc.
(4) Figures should ~e rounded off to avoid unnecessary
details in the table and
a footnote to this effect should be 'given
(5) The table should not be overload d . . detai.ls, rather a number of tables
should be prep d E. e wilh
are . ~ach table sho Id be
particular purpose. u complete in itself and serve a
 r 29

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I :,t}
tJJ .. ~,,.
' '"" ' ,mr,or Jln
I

r ()
(I ) i,m e ""'''''_. it( C , V" rial,l e t,avt th ht: ,;r
r,pfm..,,1,v1 ,
0 I '' a . ••; ,11 rq,r~Y!rJt r:;.
va lue, t;, ·"rJ
mrn imum I Uti1 when ,t f>t,.b,rn_ -,. . ,
'..,
hl"..I.)
, ':~
" . .
(2) lhuad ,cr1,pl111Mcnt P vc t,m t penr N ,,
, cmnpone for •ucce1•1
" , r,r1 f:i*- ~,,
untl ,,,. ch art It C-O n4 1'.t , (Jf thru cur1'tf. · ..-::-~
, k wn a.h 7 ,t t
(3) z. cbart rn al n-<>
no
, of alI typt ., are ,rty rr; ..f:" '.':I"'· ,,''}J
a.xiN. 1•ue11 cy di ,,tributfo n , _
,,,a.ph · J7r1•..,
(4) Jfretf uency ,. •
ly (or th e w. m e ,e a ~ ~ r wh1cb V ~ :1, c~
fo
mc:m ,i of graphs precise e lcnr,wn ~ fr ~ ~tt.:.,;
s of da ta . Su ch gr apm ar
plotted for other type
graph,4'.
n of graph
MtthodA of preparatio are fre qu en cy graph~ Lt i~ prep-q«
essential w prep
Some ba.~k knowledge is al lin e js ca lle d Abs<.L~ i.e X-aJ; n
c~. 'The ho riw nt
with the help of two Jjn ve rtica l lin e called Ordin.att i.e .
t variabl e an d the
representing independen e m ee tin g pojnt of X and Y a.x is
i!
t variable. Th
Y-axis representing dependen
point.
caJJcd Zero (0) or origin e ze ro po in t (O J is positive (+) and le
ft
i, fro m th
The right pan of 'X' ax of 'Y ' axis from zero poim
u
kewise the up pe r part
part is negative (-). Li 'X ' an d 'Y ' axis intersect each
~
r pa rt is ne ga tiv e.
positive while the Jowe pa rts . Ea ch pa rt is called Qu.ad
rar.:
is divided into 4
at 'O' point and graph t w he re 'X ' and ' Y ' both axis
are
d fir st Q ua dr an
Upper right part is caJJe Q uadrant Here 'X ' axis
is negati ve
rt is ca lle d se co nd
positive. Upper left pa w er left part is called tltird
Quadran t
ive (+ ). Th e lo
(-) and 'Y ' axis is posit e. Th e lower right part is
known as
' ax is is ne ga tiv
where both 'X ' and 'Y sit iv e (+ ) an d ·y · axis is negative
(- ).
'X ' ax js is po
fourth Quadrant where hic al re pr es en tation of st.arisiical data.
used for gr ap
Mostly first quadrant is
where both axes are po
sitive.
y

I st Quadr.1J11 (+) I'

2nd Quadrant (+) I
I
(+)
(-)
X I
X'

(-)
0

4ch Quadrant
(+ )
(- )
I
I
3rd Quadrant H

Y'
rant
·x· and ·y· .intersecting int producing 4 quad
Two axes each other on 'O ' po
 , / 1
( ••I re fu
111 ,mil N t'f• f"r \t~l1 '1 1l lf ►fl "' n,,,u I JI
ItnH• of ,1'........... ucm
, ,, lf\lt' unit hni llm, hi gmJ>h
l\\tJ\lht'd lo pJtlf(mt tho /41nllst1rnl datH in
ANITT 1 . '
,•• , '"'" tms tu sh\l\\' ht11tt' numht'I~ r
m ch n~ 500, HX>0, 2000 und ohovo
SUl'111 ,n '
.,,..,,., lht\n tu~ hn" lo ron~lllcr I cm Ion~ lino on ~mph ns ~00 unit bW' line
tit'\ -~" t . '
N,,w I ,,111 Is cfh1itlod ~ t.i111t.'s lo ropro~onl 500 unit hor lino. I cm is denoted
• • , L' II\ 1,s tO; J cm nN l ~ null No ou. For number 7~0 n point in hctwccn
1\8 .Ji ,,
~ ,.oJ to '" mri111loncd. ·n,o
snaue m~thod con he ndoptcd to represent any
numhtr,
Groui_,ed d11l11 rau be tt1,res, nted arophkally In ,my
one or cllt' rollowlna WllJ~
(I) IUslo~nun (2) Jlrol1uoncy polygon
()) Frcqu~ncy curve (4) Rolntivo frequency mup
(') rumulntavo f1'C(1uoncy curve or ogive nncl (6) Seutter or dot dingrnrn
I. IIL~hllrftlll, Thi s srnph is used for continuous frequency distribution .
rn1t, width of the class intorvnl markod nlong with the X-nxis, or abscissa. On
thoso lonltlh. roctnngles of nrcns proportional to the frequencies of the
N•P"divc dil.~s intervals nrc erected.
1f tho clnss intcrvnls nro of equal l~ngths. the~ the heights of the rectangles
arc prnp<,rlionnl to the corresponding frequencies and for unequal class
lntorvnls, the hoights of the rectunglcs aro proportional to the ratios of the
frequo~1dl~s 10 the width of tho corresponding class.
Following grouped dutn is obtained in an observation of "rate of
rt•production" of 50 fishes of u species. Make n Histogram, Frequency polygon
omJ Frcqucru:y curve with the help of dntn provided.

<.:I•• lnlervobl 0- lO l(}-20 20-30 )0-40 40-50 50-60 60-70 70-80 8~90
t'l'liquency 1 4 7 8 9 9 2 6 2
--------
Solution OX-axis cm ::: 10 class interval denoting the rate of
rc11roduction
OY-uxis I cm ; : : I frequency representing the frequency of rate of
reproduction
rhe frcquency of Ist class interval O - IO is 3 which is being represented
by 3 cm. = 30 small squares on OY axis because 10 small squares = I
frequency. In the same fashion rectangle for each class interval and frequency
is plotted and finally a histogram of the above frequency distribution is shown
in Pig. 4.1.
 [/ec tWn u,, ... • • .,,,. ~ ~ ' "'l-1 /l() f
I ()'
C0
cm 7cm 8cm 9cm 1Ocrn
6 80 00
60 70 1Oo
32 1

y . axis
9
8
7
ij' 6
~ 5
~ 4
1 3
2 ) - X - axis
l __L j__30l--}40::--50;:~60fn-70-fn80~~~90WC
100
o 10 20
.
rate of reproduction
their frequency of
. gram showing rate of reproduction and
Fig. 4. J. Histo
50 fishes of a species.
ve. Tl:e values .of the Vari ~k
. Frequency polygon and 3. frequency · cur d . fr
2 b _sae an tnetr equencies are lakcn
for an ung:°"ped data are taken as the a sc1s
, the m1d-pomts. ofb'the class intervals
as the onimates . For a grouped fidata d arc
. ae. Then a requency poIygon 1s, o tame by joining th
taken as the absciss
class inteivals are of small le '
plotted points by the straight lines. If the ~'
then the plotted. points are joined by free hMd. The curve so obatined is kn ~
.
Y· axis
E

~5
C
Q)

5- 4
l
2
1

60 . 70 80 90 100 X-. axis

o 10 20 30 40 50

Fi
rate of reproduction
g. 4.2. Frequency polygon and freq
50
~ .or fishes of a species of ::~Y
curve showing rate of rqm,duction and
their

en Imes Joming mid pom .

polygon ts A, B, C, D, E, F, G, H and I of rect angle show the frequency
Broken lines · • . .
.. Jommg mad p . represent
omt~ A to I of rectangle
Joming the mid-points of class r ho . . the frequency curve. It is drawn by
intervals of uppe
(BC- H' rectangle by free hand.
nzontal Imes of
at a glance. Nutncrous u1agnu11~ an: u :">cu ,n 01u111cu-1c ana1ys1s . i mportant types
of diagrams used for presentation of data are given below:
(1) Linc diagrruns
(II) Bar diagran1s
(Ill) Pie-diagrams or Pie chart

[I] Line diagrams

This is the simplest type of diagram. For diagrammatic representation of data,
the frequencies of the "iscrete variable can--be ptesented by a \ine diagram. The
variable is taken on the X-axis, and the ,,frequencies of the observation on the
Y-axis. The straight lines are drawn whose lengths are proportional to the
frequencies.
Worked examplt __: The frequency distribution of a discrete variable (RatJ
of reproduction 6f 50 fishes) is given in the following table 4. 1·4.

Table 4.14
Rate of reproduction 10 20 30 40 50 60 70 80 90
Frequency 3 4 7 8 9 9 2 6 2

The line diagram is given in Fig. 4.7 of the data presented in above Table 4.

9 -
8 -
7 ...
>,
-·
g -
6
5
I

&4 -
Q)

-!
3-
2- '

1-

0 10 20 30 40 50 60 70 80 90
rate of reproduction
Fig. 4.7. Line diagram.
[II] Bar diagram
Bar diagrams are one dimensional ·diagrams because the length of the
important, and not the width. In this case the rectangular bars of equa
is drawn. .
 diagrams ljJ re 1 ....i:,- - - - ...,
- ·-r · - uc u a1ag
r . -,
.JI:,. ram. A ll\y '\
simple bar di• agram • '¾
t. S11• 11P le bar u- g 1s usedatns
tO p
. bl As one b ar represents only one ti1gur
one varia rep
X::o''
e. e, there are
t the .
nwnber of figures.. For example a s1. mp le bar . tc ~11
diagram (F ioas tl\at\'J \ l'l
\,.,_
of following exampl •t~ ) ,~·'II\
··
taking data e. . . C:, •

\ Worked e~am
le Oxygen co nsumpuon m cc/k . 1\1\\
g/h m different
ear in a species opf 6• h was obtained as below. Dra
y is w a simple b tl\\)~\\\\
M ~\
J-98 F-98 A-98 M -98 J-9 ar d\a ,
-98 8 J-9 8 A- 98 S-
~
Months 98 0- 98 N.90
67 100 105
85
1, ~
0
V0 1 74 84 95 90 90 b -ll ,
78 74 t
consumed G4 l
~l c.

110 \ 0
Q)
100 ~

~ □ aa
t, 90
ai

nn□ Lh~J~
~
~
§, 80
0 70
> 60
50 Jan. Feb. Mar. Ap
r. May. Jun. Jul.
Aug. Sep. Oct.
98 Nov. Dec. Jan.
Fig . _ _Simple ba 99
48 r diagram showing
oxygen co ns ~p tio
in different months n in a sp ec ies of
of a year. fish recorded
2. Divided bar
diagram. Th e fr
co,mponents and su equency is di vi
ch a diagrammatic de d in to diffettn\
diagram . Suppose re pr es en ta tio n is ca
we have to show lle d a divided bat
fishes in different the average pr od
years, the data ca uc tio n of fo ur species ot
Each bar then wou n be re pr es en te d
ld be divided into by di vi de d ba r dia
four pa rts and ea gtam.
the mean productio ch pa rt w ou ld rep
n of each fish spec resent
Average catch in ies.
metric tonnes of W
the year 1993-94, allago, Ctztla, Cirhi
1994-95, 1995-96 nna & Clarius for
(Hypothetical data) an d 1996:.97 in In
. di a w as as fo\\o
ws
Years Wallago Calla Cirhinna
1993-94 Clarius Total
1383 634 513
\
1994-95
2021 1383
400 2930
1995-96 521
1914 313 4238
1996-97 1413
2664 551
1636 900 4518
424
26S 4989
 1
I 39

l--'-'----~__.: ~,~
(_______....-A}OrfWlN ; -a.nus
C

§
\00
(

90
\C..

h g
i
~
80
70

60

8
0
i 50
40
·o
~
0
30
0
8 1000- = 0
C
20
C
101 0 10
...Q
e
!
•e> :l 93-~ 94 .95 95 -96 96 -97 •>
0 93- 94 94 -95 95 - 96 96-97

~-ears
years

F~ 4.9_ Oi\iliro b a r ~ ~ ag the fig. 4_10,_ Pacaugc di\;ded bar 5>agram

~ of fishes of ~ species in fua. *CfNescatmg 111e ctan or fish prodDaD ~
~~GVS,._ 4 • · ic s in 4 dilfemll years..

3. Percentage bar diagram. The length of bars is kept equal to l 00 and

me diYisi-ons of the har correspond to the percentage of different components...
Each \.--ompooent of the b3:f diagram indicates the average catch of fishes. Nix:Ne
ixr-=-~: ~~ di,ided bar diagram (Fig. 4.10) ls drawn to rq.tesent ~ above daa..
4. ~lultiple bar ~oram. 'When a comparison between two or m<n
relaterl Yariab}es has to~ made, then multiple bar diagrams are preferred- The
t_echnique of simple bar diagrams qlI\ be extended to represent two or more sets
of in.terrelated data in a diagram_
1'1orled uampk : Value of three haematological parameters \"II- RFCs
count.. Hb':l- and PCV of a species of fish \\"aS studied for \ 3 months (Between
Jan ·95 to Jan ' 96). Data obtained is given below to draw a mu\tip\e bar
diagram_
1 1

J-95 F-95 ~t-95 A-95 M-95 J-95 J-95 A-95 IS-<}5 0-95 '. N-95 ,D-95 J-96 \
\ \ ' I \ \

2-01 2.01 2-~ 2-12 215 , 2.46 1.27\ L81 t 1.91\ DOI 2-19, 2. U \ 1.04\
\ \ \ \ \ I \

\
&.5 8.6 &.8 9.l \ 1.1 12.6 11.3 \ 9.i 9.6 tu , n .& tO.9 g_6
Bb'fe I

, (m&{l00ml} I l \I \
I
14.1 14. l 14.1 ' \4.4 I }6.6 19.6 26..2 24.9 14.4 \ 14.5 ~ .6 124.l \4.0
PCV {")
l \ \ I
('o llrnfon mu/ Hr/""'"''"'"''"" of /)aw I 4l
j 111 J Pit t•hart (ff (hart) or ptf dlaanam or 11tctor dlaknun
It is "" rn~y wuy of proso1HtnM ,hscrotc dotn of ,1u"lhu1iv~ chnrnctcrs such ns
blood ~roup~. Rh Ou:1rn1, u~c groups, ~o.ll group etc. Thr frequendeN of the
gwups 11rr 5hown in n drdo . Do(lrr~N of nngle dcnolo the, frt,<1uency ond aren
nf tho ~cctor. h pteNNlts compnrntivo dlfforonn.i tll 11 Jtlnnce. Si1.c of c"ch angle
is <'n h;ul&,ted hy multiplying the clnss (lCl\:t,ntngc with 16 i.e., 360/ I()() or hy
the followin~ fonnulR :
. . Clnss frc<1,,cncy
S11,0 ot the angle 0 • - - ; x 360°
lbtal observations
(Pie chart alwayiS represents the dut11 in percentage)
Worked ,xampl,. In a st.udy of hlood groups in 1629 males und 1181
females of Bihar stnlc following data were obtained -

Tobit 4.16.
- - - --
Blood 1roup1 No. of persons Perccnta1c Degrees
---
Male 1-~emale Total

A 427 317 744 26.5 94.4

B, 5,9 412 97 1. 34.5 124.2

0 521 367 888 31.6 11 3. 8

AB 122 85 207 7.4 26.6

Total 1629 1181 2810 100.0 360.0

A
B
744
{26.5%)
971
{34.5%)

0
888
(31 .6%)

Fig. 4.13. Pie chart or sector diagram showing

distribution of blood groups as given in table 4.16.

Size of angle for blood group A in tabl~ = 26.5 x 3.6

744
= 95.4 or x 360 = 95.4
2810
Pie chart can be drawn showing distribution of blood groups as giver ·
table 4. 16.
 J11'1~ · . . · -. ,.... ~\, on ·
r,Ll sarnvle. The selected pan of ' ..
. 1 . «\ popuht\lnn i , k . .
18uon a ways means the tot• . s nown ag sa mple . \ n stat ,st ,c1-,,
orLI ' . 1
P . inferences arc to be made tlt nun,bc. r of .m d'1v1dual .
observatio n~ lrom
wh'c11 . f . a a pm11cu\ a.r t
sf11a
II co11cctl0n
. .
° the popul ati on h' . ' imc . A sample rc prcl\cnts the
w H:h Ins a
· pie, all paucnL" of AI DS of lh . \
· ctua ly been ohscrv cd . Por
~o rfl . c world rep •
c . idual o bservation s on
•nd,v .
loor 20
or 30 (any .
·resent~ a populati on, whcrcab
.
1 the po pulatio n re fer to a sam ~ . conveni ent number) patie nts
frofll f , p1c, as dcta1 led i n h
oata. A set o values recorded .
1or an event . , c apter \\ d
3.
•sties arc generally based on . ct· . is ca c data. 'The data in
stall tn 1v1dual obs •
. tients suffering from Kalazar was me erv attons. The Hbo/o of \()
P~ , 9.5, 8.9, 8.8, mg/JOO ml. Herc ;~red as l0.2, 9 .6, 8.8, 10.7 , 9 .9 , 10.3,
1 ·3 for an event i e Hbm d .
1
· ' 9 ·6 ······ ·8 ·8 mg/100 m\. are a set of
value 5 · · -m an is called d t Wh'\
·h ds we come across · a a. 1 e !;tudyin g statistical
rr,et o , numerous data Th d ·
·s do not consist of " . · e ata co\\ected for statistical
analYs' observations that are identical, since there wou\d be
l1·ttle reason
. ·nto study such
h
a variation Th d
· e ata counted for the purpose of
analysis ~• . represent l e varying values of variable i.e. a characteristic that
shows van,ation .
A. data
. collected by .person a\ ·mvest1gat1on
· · from the ongma\•• source, b)'
performing some expenments is called primary ·data. For · biological
researches, data collected only from persona\ experimental study i.e. primary
data is used . Data is of two types -
(a) Qualitative. According to quality or attributes the data is ca\\ed
qual itative. For example, lions of Gir sanctuary of Gujrat State are to be
classified in respect to one attribute say sex, in two groups, one is-of male and
the other is of female.
(b) Quantitative. According to magnitude the data is ca\\ed quantitati vc
For example, chickens of a poultry farm may be classified on the basis of thei
growth rate. Quantitative data may also be classified into two types -
( i) Continuous. Values of variate do not exhibit any breaks or jumps. F
example the increasing length and weight of a child.
( ii) Discrete. Values of variate vary by infinite jumps. For example 1
oxygen consumption of rat '{Rattus rattus) of different weight groups "
measured as 500 cc/h/100 ml, 600cc/h/\OO ml, 620 cc/h/100 ml, 680 cc/hl
ml and so on.
Observation. Measuremen t of an event is called observation. For inst2
1
blood pressure, temperature of body, oxygen consumptio: etc. are e
whereas, 160 mm & 80 mm (upper and lower pressure_), 106 F, 65 ~g/hou
· · · To urce that gives observat\ons S\
ml are their respecu ve observations . e so
 . I 'ferm.} w,u ..) ymt>ol s
tis/l CO
~ [5
ossible to observe al I the v I
· r, ol p · nlimited ·1 · a ucs o f a vari b\ · - . -
,s ulatioO 15 u ~ size e .g. the numbe a e, 1t ts infin ite . An infinite
poP of zooplanktons in sea and r of RBC' s in human body the
f11ber • so on •
rtll ,nple. The selected part of a ·.
511 _. Population is k.
uon a1ways means the total nown as sample . ln statistics
ooll 1a . number of i d. . . . ,
P ~ h 10 ferences are lo be made at . n ,v,dual observatiom trom
~ t,1C . f th a Particular ti
all collecuon. 0 e population which has me. A sample repre~nts the
sfll le, all patients of AIDS of the actua\\-y been observed. For
~afllP . world repre
e, . •dual observations on 10 or 20 sents a p-opu\ation whereas
. dt''t . or 3O (any . '
,ri the population refer to a sample d . convenient number) patients
froflloata• A set of values recorded ,fas et.ailed i~ chapter 3.
or an event \\
. u·cs are generally based on ind·1 . d is ca ed data. The data in
5
5tat1. ots suffering from Kalazar was meas v 1 ua\ obse ·
ed rvations. The Hb% of 10
pat~e 9.5 , 8.9, 8.8, mg/100 ml. Here 10 2ur 9 6as 10.2, 9.6, 8.8, \0.7, 9.9 , \0 .8,
11 · ' · · , · ....... 8.8 mg/100 m\ are a set of
1 es for an event i.e. Hb% and is call d d . :
va O e ata. While studymg statistical
me.thods, we come .across.. numerous data · The d ata collected. for statistical
Jysis do not consist of observations that ar 1·d •ca1 .
ana e enu , smce there wou\d be
little reaso~ to study such a v~ation. The data counted for the purpose of
ana\vsis
; will. . represent the varying values of van·ab\e 1.e.
• a charactenstic
. . that
shows vanation.
A. data
.
collected by .personal . investioation
e
from the ongma
· · 1 source, by
performmg some expenments 1s called priniary ·data . For · b.101og1ca · 1
researches, data collected only from personal experimental C''tudy ; e pnmary
•
·
.., t. • •

data is used. Data 1s of two types -

(a ) Qualitative. According to quality or attributes the data is callee
qualitative. For example, lions of Gir sanctuary of Gujrat State are to b
classified in respect to one attribute say sex, in two groups, one is -of ma\e an
the other is of female.
(b) Quantitative. According to magnitude the data is called quantitati,
For example, chickens of a poultry fann may be classified on the basis of th
growth rate. Quantitative data may also be classified into two types -
( i) Continuous. Values of variate do not exhibit any breaks or jumps.
example the increasing length and weight of a child.
(ii) Discrete. Values of variate vary by infinite jun,ps. For example
oxygen consumption of rat \(Ratti,s rattus) of different weight groups
measured as 500 cc/h/100 ml, 600cc/h/\OO n1\, 620 cc/h/\00 n,\, 680 cc1'
ml and so on
Observa~on. Measuren1ent of an event is called observation. For im
blood pressure te1nperature of body, oxygen consumption etc. are
'
whereas, 160 rnn1 & 80 mm (upper and lower pressure), 106°F' 65 k. g/he
. Th . e that gives observaoons
ll11are their respective observattons. e sourc