We have
already seen how to collect the data about the behaviour of a group. The information is in the form of
questionnaires and schedules. These
questionnaires and schedules must be edited first. Some of them may contain erroneous data; some
contradictory statements might be present in some. We have to determine which of the statements
is correct. In case of doubt we may be
required to delete the whole questionnaire form. Even after this is done, the data are very
large and just by going through them no conclusion can be drawn. For most people it is difficult to see
relations and patterns in raw data. The
characteristics of a group of raw data must be summarized to make them
comprehensible. Therefore, to make the
data under-standable and comparable, classification is necessary. This also provides a basis for decision
making. We classify the data according
to certain characteristics and tabulate the information.
The data can
be presented in any of the following forms.
They may be:
1.
incorporated in a paragraph of text
2.
put into tabular form
3.
expressed graphically
1. Text
Presentation: It is not very
effective since it is necessary to read the whole paragraph very carefully, and
most people will not be able to understand the data in this form easily. Following is an example of text preparation.
A survey was conducted amongst one lakh
spectators visiting, on a particular day, the cinema houses showing criminal,
social, historical, comic and mythological films. The proportion of male to female spectators
under survey was three to two. It
indicated that the respective percentage of spectators seeing criminal, social
and historical films was sixteen, twenty-six and eighteen. The actual number of female viewers seeing
these types was four thousand six hundred, twelve thousand two hundred and
seven thousand two hundred and seven thousand eight hundred respectively. The remaining two types of films, namely
comic and mythological were seen by forty per cent and one per cent of the male
spectators. The number of female
spectators seeing mythological films was four thousand four hundred.
2. Tabular
Presentation: This method is
better than the previous method. With
its headings for rows and columns the table is easier to understand. The data presented in the above text can be
presented in a tabular form as follows:
|
Types of
film
|
Number of
spectators
|
||
|
Males
|
Females
|
Total
|
|
|
Criminal
|
11,400
|
4,600
|
16,000
|
|
Social
|
13,800
|
12,200
|
26,000
|
|
Historical
|
10,200
|
7,800
|
18,000
|
|
Comic
|
24,000
|
11,000
|
35,000
|
|
Mythological
|
600
|
4,400
|
5,000
|
|
Total
|
60,000
|
40,000
|
1,00,000
|
The
advantages of tabular form can be easily seen, if we compare the data in the
above table with the data in the paragraph given. Both the table and the paragraph contain the
same data, but they are more clearly represented in the table.
The data are
classified and then presented in a tabular form. There are a number of ways of classifying the
data, but the possible classification can be grouped into the following four
types:
- Classification based on Differences of kind
- Classification based on Differences of Degree
- Geographic Classification
- Time Series
1. Classification
based on Differences of Kind: A
business concern may sell a variety of products. Information of sales of different products is
a common requirement. Here the sales are
classified according to different kinds of products. The classes are set up on the basis of qualitative
differences. The following are the
examples where this type of classification is used.
- Sales classified according to terms of sale –
cash, credit
- Sales classified by salesman
- Employees classified by types of work done
- Products classified as defective or non
defective
- Population classified by religion
- Exports classified by commodities
No. of
students in a college
|
Male
|
2000
|
|
Female
|
1000
|
|
Total
|
3000
|
This table considers only one characteristic, namely
sex. The following table considers two
characteristics and classifies the workers in a factory.
|
Type
|
Number of
workers
|
||
|
|
|
|
|
|
Permanent
|
|
|
|
|
Temporary
|
|
|
|
|
Total
|
|
|
|
Similarly, we
can consider three or four characteristics in a table.
2. Classification
based on Differences of Degree: If
households are classified according to income received in 2000, we get a
classification of this type. Here the
classes represent varying degrees of income, and all households having income
between certain specified amounts are placed in the same class.
This
classification will be quantitative, as the differences of degree will be
expressed in quantitative terms.
Sometimes such classification is done on qualitative terms, but that is
not usually satisfactory. Employees may
be classified as young, middle aged and old.
But this classification is not very clear. The following are examples of classification
of this type.
- Classification of a group of persons according to
age.
- Customers of a store classified according to
amount of annual purchases.
- Retail stores classified according to yearly
volumes of sales.
- Factories classified according to number of
employees.
- Banks classified according to
amounts of deposits.
|
Age in
years
|
No. of
children
|
|
0 – 3
3 – 6
6 – 9
9 – 12
|
10
20
25
15
|
|
Total
|
70
|
3. Geographic
Classification: This separates the
data into groups according to the continents, countries and other geographic
subdivisions. Productions of rice in
different states in India
Rainfall in
some states in India
|
State
|
Rainfall
(in cms)
|
|
Andhra
Pradesh
Kerala
Chennai
|
105
125
120
100
|
4. Time
Series: Here the data are classified
on the basis of time intervals and arranged in the order of occurrence. The following are the examples of time
series.
- Yearly exports of
- Number f books borrowed by students every week in
a college library.
- Total strength of a college for years 1990 to
1997.
The following
table gives the yearly production of a factory for the years 1990 – 91 to 1994
– 95.
|
Year
|
No. of
units (in ‘000)
|
|
1990 – 91
1991 – 92
1992 – 93
1993 – 94
1994 – 95
|
30
35
33
37
39
|
Descriptive Characteristics
There are
certain characteristics, which are not capable of numerical measurement, eg.
Blindness, literacy and smartness. These
are descriptive characteristics. These
are also called attributes. The persons who possess the characteristic
are placed in one class and those who do not possess it are placed in another
class.
If we
consider only one characteristic at a time, we have simple classification, ie.,
if we consider only blindness we have simple
classification. But if more than one
characteristic are considered simultaneously, we have manifold
classification. If we divide a group of
persons according to sex and age group in addition to blindness, we have
manifold classification.
In this type
of classification the classes should be determined clearly. For example, if we are considering literacy
we should decide whether we call a person literate if he knows only how to sign
or should be able to write and read according to certain standard. If there is no clarity the purpose of
classification is not served.
Numerical Characteristics
Certain
characteristics can be measured quantitatively.
If we consider the heights of 100 students, the height can be measured
numerically and it will vary from student to student. Therefore height is called a variable. Other examples of variables are marks, age,
income, size of readymade garments, size of shirts, etc.
The variables are classified as discrete and
continuous. The size of shoes can be
denoted by 5, 6, 7, etc. This variable
cannot take a value between 5 and 6 or between 6 and 7. Such variables are called discrete variables. If we consider height in cms, it can take any
value in a given range. Such variables
are called continuous variables.
PARTICULARS OF TABLES
The data
classified are to be tabulated. While
tabulating, we have to bear in mind many particulars, which make the table
interesting, effective and useful.
PARTS OF THE TABLE
- Title: The title should convey clearly the
subject and the scope of the table.
It should tell us what is represented in the table. The title should be brief. It should be in series of phrases rather
that long sentences. The title
lettering should be large enough and prominent in the table.
- Captions
or Column Headings: At the
top of each column, we should write what the column represents. This column heading is known as
‘caption’. The unit of measurement
for the observations in the column should also be included in
‘caption’. e.g. Height in cms. Or export in crores of Rs. The captions may be shown in smaller
letters than the main heading. The
width of each column should be decided by the largest number to be
represented in the column and the caption should be made to fit in that
place.
- Stubs or
Row headings: Each
horizontal row is designated. These
designations are known as ‘Stubs’.
The length of the stub items determines the width of that column.
- Arrangements: The captions and stubs should be
arranged in some systematic order.
The items to be compared should be in consecutive columns. The order shows which items are to be
emphasized. The totals of the
columns are placed at the bottom of the columns and those of rows are
placed in extreme right hand column.
The principal basis for arranging the items are alphabetical,
chronological, geographical, order of size, order of interest or emphasis
and least according to custom.
- Footnote: If any explanation in the table is not
complete, it is advisable to give it in a footnote. The table as far as possible should be
complete and should not need any footnote.
- Source: Source also should be indicated at the
bottom of the table. If the user
wishes to check the data he can do so from the original source.
The following rules should be observed while preparing
a table:
- A table should be complete within itself. It should not be necessary to read
footnotes.
- It should be logical unit, and only data which
are related be placed in the same table.
- The arrangement of stubs and captions should be
such that desired emphasis is secured.
- The title should be written at the top of the
table which should be clear and precise.
- Captions and stubs should be brief and
clear. Footnotes may be added when
necessary.
- The captions and stubs may be grouped to indicate
relationship.
- Units of measurement should be carefully stated.
- Source should be stated.
- The table should be accurate; otherwise, people
will lose faith in the work as a whole.
When tables are transferred from one record to another they should
be checked properly.
PROBLEMS
1.
A supermarket divided into five main sections:
grocery, vegetables, medicines, textiles and novelties recorded the following
sales in 1961, 1962 and 1963.
In 1961,
sales in grocery, vegetables, medicines and novelties were Rs. 6,25,000,
Rs.2,20,000m Rs. 1,88,000 and Rs. 94,000
respectively. Textiles accounted for 30%
of the total sales during the year.
In 1962, the
total sales showed 10% increase over the previous year. While grocery and vegetables registered 8%
and 10% increase over their corresponding figures in 1961, medicines dropped by
Rs.13,000. Textiles stood at Rs.
5,36,000,
In 1963,
though the total sales remained the same as in 1962, grocery fell by Rs.
22,000, vegetables by Rs.32,000, medicines by Rs, 10,000 and novelties by
Rs.12,000.
- Tabulate the above information.
2.
According to
the census of Manufacturer’s report, John Smith Manufacturing Company employed
400 non-union and 1250 union employees in 1941.
Of these 220 were females of which 140 were non-union employees. In 1942, the number of union employees
increased to 1475 of which 1300 were males.
Of the 250 non-union employees 200 were males. In 1943, 1700 employees were union members
and 50 were non-union members. In 1943,
250 were females of which 240 were union members. In 1944, the total number of employees was
2000 of which one percent was non-union employees. Of all the employees in 1944, 300 were
females of which 5% were non-union employees.
3.
Of all the employees in a certain company,
one-in-three is a woman and one-in-twelve is a married woman. One-in-sex of the men is a married man, six
married men and five per cent married women are married couples.
4.
The city of Timbaktoo
There were
6,77,100 buildings of which 1,76,100 were in rural district. Of the buildings in urban district, 4,06,600
were inhabited and 4,500 were under construction. In the administrative district 4,000
buildings were uninhabited and 500 were under construction out of the total of
61,600. The total buildings in the city
that were under construction were 62,600 and those uninhabited were 44,900.
5.
The total number of accidents in Southern Railways in
1960 was 3500 and it decreased by 300 in 1961 and by 700 in 1962. The total number of accidents in meter–gauge
section showed a progressive increase from 1960 to 1962. It was 248 in 1960, 346 in 1961, and 428 in
1962. In meter–gauge section ‘Not
Compensated” cases were 59 in 1960, 77 in 1961and 108 in 1962. ‘Compensated’ cases in broad–gauge section
were 2867, 2587 and 2152 in the three years respectively. From the above report prepare a neat table as
per the rules of tabulation.
6.
At a competitive Examination, at which 600 students
appeared, boys out-numbered girls by 96.
Those qualifying for interview exceeded in number those failing to
qualify by 310. The number of science
graduate boys interviewed was 300 while among the arts graduate girls there
were 25 who failed to qualify for interview.
Altogether there were only 135 Arts graduates and 33 among them failed
to qualify. Boys who failed to qualify
numbered 18.
7.
200 women from each of the age groups 20 to 30, 30 to
50 and 50 to 60 were surveyed. 50% of the women from the age group 20 to 30 were
educated of whom 70 had a job, 60 of the uneducated women had a job. 35% of the
women from the age group 30 to 50 were educated of whom only 30 had a job,
while 100 of the uneducated women belonging to the same age group did not have
a job. 80% of the women from the age
group 50 to 60 were uneducated and no one from them had a job, while 75% of the
educated women did not have a job.
- Tabulate the information.
8. In a market survey of 25,000 women from
Mumbai, exactly one-fourth were non-Maharashtrians, 15 out of every 25 women
were employed and 70 per cent of Maharastrian women were employed.
60% of employed Maharashtrian women and
20% of employed non-Maharashtrian women were married.
The number of unmarried Maharashtrian
women who were employed was 3250 and 1435 unmarried non-Maharashtrian women
were not employed.
- Tabulate the above data.
9. A survey of 1000 persons from Mumbai
was conducted, of which 60% were Maharashtrians and the remaining
non-Maharashtrians. The ratio of total
number of men and women was 1 : 1. 50%
of the men were Maharashtrians and the remaining non- Maharashtrians. 100 non- Maharashtrian men and 50
Maharashtrian men watched ‘English’ news on television. And among women, 100 Maharashtrian women and
50 non- Maharashtrian women watched ‘Hindi’ News on television.
- Tabulate the above data.
10. In 1989, out of 2000 students, appearing
for HSC Examination at Dadar centre, 785 had opted for Mathematics and the
remaining for Secretarial Practice. The
number of girls was 150 of whom 850 had opted for Secretarial Practice.
In 1990, the number of students with
Mathematics as the optional subject was 875, of which 615 were boys while the
number of students with Secretarial Practice decreased to 1185 of which 795
were girls.
In 1991, the total number of students
increased by 150 and increase in the number of boys was double the increase in
the number of girls. Out of 1400 students
who had opted for Secretarial Practice, 935 were girls.
-
Tabulate the above information.
11. 200 women from each of the age groups 20
to 30, 30 to 50 and 50 to 60 were surveyed.
50% of the women from the age group 20 to 30 were educated of whom 70
had a job, 60 of the uneducated women had a job.
35% of the women from the age group 30
to 50 were educated, of whom only 30 had a job, while 100 of the uneducated
women belonging to the same age group did not have a job.
80% of the women from the age group 50to
60 were uneducated and no one from them had a job, while 75% of the educated
women did not have a job.
-
Tabulate the above information.
12.
In a survey about preference of cold drink (Pepsi and
Coke) in a College A, the following information was obtained. In College A, girls were 60% out of total
number of 3000 students. The percentage
of students who preferred Pepsi was 45%.
The number of girls with preference for Coke was one third of the total
number of the girls.
- Tabulate the above information.
13. A survey was conducted to find whether
there is any relation between the education of father and son. A total of 90 pairs of father and son were
surveyed. 100 sons had post graduate
degrees while the remaining were only graduates. Fathers of 50% of the sons having
post-graduate degrees had post-graduate degrees themselves, while fathers of
only one third of the remaining students had post-graduate degrees.
- Tabulate the above information.
13.
The following is the summary of the time of leaving
home and the number of hours spent in the institution of a group of teachers in
a certain institution. Present it in a
tabular form.
One teacher leaves the home before 5.30
a.m. and spends 4 hours in the institution.
Of the 23 teachers who leave their homes between 6 and 7 a.m., 7
teachers spend 3 hours, 11 teachers spend 4 hours, 2 teachers spend 5 hours and
3 teachers 6 hours. Of the 16 who leave
between 7 and 8 a.m. 4 teachers spend 3 hours, 6 teachers 4 hours, 1 teacher 5
hours and 5 teachers 6 hours. Of the 82
teachers, who leave between 8 and 10 a.m.
6 teachers spend 3 hours, 9 teachers 4 hours, 21 teachers 5 hours, 46
teachers 6 hours. Of the 21 who leave
between 10 and 11 a.m. 2 teachers spend 3 hours, 8 teachers 4 hours, 7 teachers
5 hours and 4 teachers 6 hours.
Solution:
SUMMARY
OF THE TIME OF LEAVING HOME AND TIME SPENT IN THE INSTITUTION OF A GROUP OF
TEACHERS
|
Time of
leaving
home
|
Number of
hours spent
|
Total
|
|||
|
3
|
4
|
5
|
6
|
||
|
Before 5.30
a.m.
|
…
|
1
|
…
|
…
|
1
|
|
6 – 7 a.m.
|
7
|
11
|
2
|
3
|
23
|
|
7 – 8 a.m.
|
4
|
6
|
1
|
5
|
16
|
|
8 – 10 a.m.
|
6
|
9
|
21
|
46
|
82
|
|
10 – 11
a.m.
|
2
|
8
|
7
|
4
|
21
|
|
Total
|
19
|
35
|
31
|
58
|
143
|
14. 60 per cent of the population of town A
are males, 80 per cent of the males and 30 per cent of the females are
non-vegetarians. – Tabulate this data.
Solution:
POPULATION OF A TOWN
|
|
% of
Population
|
||
|
Vegetarian
|
Non-Vegetarian
|
Total
|
|
|
Males
|
12
|
48
|
60
|
|
Females
|
28
|
12
|
40
|
|
Total
|
40
|
60
|
100
|
15. 60% of the pilgrims in a conducted tour
arranged by Asha Travels are 60 years or older; 30% are 40 years or above but
less than 60 years. The rest are below
40 years. The percentages of females in
these three groups are 10, 25 and 30 respectively. The number of female pilgrims in the last
group (below 40 years) is 12.
-
Tabulate the above information.
16. A survey of 1500 workers in a factory
gave the following results. Tabulate the
information.
One
third of the workers were females; 80% of the female workers were below 40
while the percentage of male workers below 40 was 50. 80% of male workers below 40 were skilled and
the remaining unskilled. 40% of the male
workers above 40 were skilled and the remaining unskilled. 40% of the male workers above 40 were
skilled. There was no skilled female
worker above 40 while 50 percent of the female workers below 40 were skilled.
SOLUTION:
DETAILS OF WORKERS IN A FACTORY
|
Age
|
Male
|
Female
|
Total
|
||||||
|
Skilled
|
Unskilled
|
Total
|
Skilled
|
Unskilled
|
Total
|
Skilled
|
Unskilled
|
Total
|
|
|
Below 40
|
400
|
100
|
500
|
200
|
200
|
400
|
600
|
300
|
900
|
|
Above 40
|
200
|
300
|
500
|
0
|
100
|
100
|
200
|
400
|
600
|
|
Total
|
600
|
400
|
1000
|
200
|
300
|
500
|
800
|
700
|
1500
|
17. In the annual report of a mobile company,
it is indicated that the company drilled a total of 882 wells in 1977 and 487
in 1978. Two types of drilling
operations were conducted, wild cat and developmental. In 1977, a total of 40 wile cat wells and 842
developmental wells were drilled; the comparable figures for 1978 were 46 and
441. There were 3 possible outcomes when
a well was drilled – oil, gas or dry hole.
Of the wild cat wells drilled in 1977, 6 resulted in oil, 4 in gas and
30 in dry holes, the comparable figures for 1978 were 6, 4 and 36. of the developmental wells drilled in 1977,
660 resulted in oil, 77 in gas and 105 in dry holes, the comparable figures for
1978 were 300, 77 and 64.
- Tabulate the above information.
18. Out of a total number of 2000 candidates,
interviewed for employment in a company at Nasik, 628 were from Pune and the
rest from Nasik Nasik Nasik
-
Tabulate the above information.
19. There are two families x and y whose monthly average expenses are classified under five heads
(a) House rent (b) Household (c) Education (d) Medical and (e)
Miscellaneous. Family x spends Rs. 1500/- as monthly house
rent whereas y spends Rs. 1000/-
only. Family x spends twice the amount under the head (b) as y spends on account of (a). Expenditures under (c) are Rs.400/- and
Rs.500/- where x spends more than y.
Medical expenses of family y
are Rs.50/- more than that of x. Total expenses under the head (e) of the two
families taken together are Rs.500/- Medical expenses of x are half its expenses under (c).
House hold expenses of family y
are six times its expenses on account of (d).
Total expenses of family x
are Rs.4600/-
-
Tabulate the above information.
20. Out of the total number of 1807 women who
were interviewed for employment in a textile factory of Mumbai, 512 were from
textile areas and the rest from the non-textile areas. Amongst the married women who belonged to
textile areas, 247 were experienced and 73 inexperienced while for non-textile
areas the corresponding figures were 49 and 520. The total number of inexperienced women was
1341 of whom 111 resided in textile areas, the number of experienced unmarried
women in the textile and non-textile areas were 154 and 16 respectively.
