Chapter : 2 CLASSIFICATION & TABULATION


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:
  1. Classification based on Differences of kind
  2. Classification based on Differences of Degree
  3. Geographic Classification
  4. 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.
    1. Sales classified according to terms of sale – cash, credit
    2. Sales classified by salesman
    3. Employees classified by types of work done
    4. Products classified as defective or non defective
    5. Population classified by religion
    6. 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.
  1. Classification of a group of persons according to age.
  2. Customers of a store classified according to amount of annual purchases.
  3. Retail stores classified according to yearly volumes of sales.
  4. Factories classified according to number of employees.
  5. 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, population in different states are examples of this type of classification.
Rainfall in some states in India 1997 – 98
State
Rainfall (in cms)
Andhra Pradesh
Kerala
Chennai
Maharashtra
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.
  1. Yearly exports of India from 1971 to 1973
  2. Number f books borrowed by students every week in a college library.
  3. 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
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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:
    1. A table should be complete within itself.  It should not be necessary to read footnotes.
    2. It should be logical unit, and only data which are related be placed in the same table.
    3. The arrangement of stubs and captions should be such that desired emphasis is secured.
    4. The title should be written at the top of the table which should be clear and precise.
    5. Captions and stubs should be brief and clear.  Footnotes may be added when necessary.
    6. The captions and stubs may be grouped to indicate relationship.
    7. Units of measurement should be carefully stated.
    8. Source should be stated.
    9. 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 was divided into three areas, the administrative district, urban district and rural district.  A survey of housing conditions was carried out and the following information was collected.
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.  Amongst the graduates from Pune, 350 were experienced and 80 were inexperienced.  While, the corresponding figures for undergraduates from Nasik, were 615 and 52 respectively.  The total number of inexperienced candidates from Pune and Nasik were 175 and 192 respectively.
            -    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.