Table of contents

Sl.No Topic

1 Meaning and definition of classification

2 Functions of classification

3 Characteristics of good classification

4 Objectives of classification

5 Modes of classification

6 Meaning and definition of tabulation

7 Objectives of tabulation

8 Components of tables

9 Requirements of good statistical tables

10 Types of tables

11 General purpose and specific purpose tables

12 Advantages and disadvantages of classification

And tabulation

Topic: Meaning and definition of classification

Functions of classification

INTRODUCTION

The collected data is usually contained in schedules and

questionnaires. But that is not in an easily assailable form. The answers will

require some analysis if their salient points are to be brought out. As a rule,

the first step in the analysis is to classify an tabulate the information

collected, or if published statistics have been employed rearrange these into

new groups an tabulate the new arrangement. In case of some investigations,

the classification and tabulation may give such a clear picture of the

significance of the material arranged that no further analysis is required.

They are however very important whether they complete the analysis or

form only part of it. The questionnaire may have been very carefully drawn

up and the whole information displayed in tabular form, no one will be a

great deal wiser as to the contents of the replies.

MEANING OF CLASSIFICATION Classification is a process of arranging data into different classes

according to their resemblances and affinities. The arrangement of a huge

mass of heterogeneous data into homogeneous groups facilitates

comparison and analysis of the data. Classification prepares the ground for

the proper presentation of statistical facts.

After collection and editing of data the first step towards further

processing the same is classification. Classification is the grouping of

related facts into classes. Facts in one class differ from those of

classification. sorting facts on one basis of classification and then on

another basis is called cross- classification. This process can be repeated as

many times as there are possible bases of classification. Classification of

data is a function very similar to that of sorting letters in a post- office are

sorted into different lots on a geographical basis, i.e., in accordance with

their destinations such as Mumbai, Calcutta, Kanpur, Jaipur, etc. They are

then put into separate bags , each containing letters with a common

characteristic, viz., having the same destination. To take another example,

when students seek admission in a college they submit applications to the

office. The applications forms contain particulars about their performance

in the previous examinations, their date of birth, sex, nationality, etc. If one

is interested in finding out how many first, second and third class students

have joined the college, one may look into each and every form and note

whether it relates to a first class student, second class student, etc. He may

find that out of 1,000 students who took admission 50 had first class ,800

second class and 150 third class. The process with the help of which this

information in a summary form is obtained is called the classification of

data.

DEFINITIONS

“Classification is the process of arranging things (either actually or

notionally) in groups or classes according to their resemblances and

affinities and gives expression to the unity of attributes that may subsist

amongst a diversity of individuals.”

- Conner

“Classification is the process of arranging data into sequences and

groups according to their common characteristics, or separating them into

different but related parts.”

-Secrist

FUNCTIONS OF CLASSIFICATION

Bulk of the data

Simplifies the data

Facilitates comparison of characteristics

Renders the data ready for statistical analysis

Topic: Characteristics and objectives of Classification

CHARACTERISTICS OF CLASSIFICATION:

The classification of data is decided after taking into consideration the

nature, scope and purpose of the investigation, However, an ideal

classification should have following characteristics:

1. Unambiguous:

It is necessary that the various classes should be so defined that there is

no room for confusion. There must be only one class for each element of the

data set. For example: If the population of the country is divided into two

classes, say literates and illiterates, then an exhaustive definition of the terms

used would be essential.

2. Stable:

The classification of a data set into various classes must be done in

such a manner that if each time an investigation is conducted, it remains

unchanged and hence the results of one investigation may be compared with

that of another. For example: classification country’s populations by a

census survey based on occupations are defined in different ways in

successive censes and, as such, these figures are not strictly comparable.

3. Flexible:

A classification should be flexible so that suitable adjustments can be

made in new situations and circumstances. However, flexibility does not

mean instability. The data should be divided into few major classes which

must be further subdivided. Ordinarily there would not be many changes in

the major classes. Only small sub-classes may need a change and the

classification can thus retain the merit of stability and yet have flexibility.

4. Exhaustiveness:

A classification is said to be exhaustive if there is no item that cannot

be allotted a class. Classification must be exhaustive in the sense that each

and every item in the data must belong to one of the classes.

5. Mutually exclusive:

Different classes are said to be mutually exclusive if they are

overlapping. When a classification is mutually exclusive, each item of the

data can be placed only in one of the classes. Example , Classification of

students among smokers, non-smokers and females is not proper since

females could also come under both the classes. Proper classification would

consist in grouping the population among males and females and further

dividing the two groups among smokers and non – smokers.

6. Suitability:

The classification should be suitable to the objective of

investigation. For example, if investigation is conducted to inquire into

the economic conditions of workers it will be of no use to classify them on

the basis of their religion.

7. Homogeneity:

A classification is said to homogeneous if similar items are placed in a

class.

8. Revealing:

A classification is said to revealing if it brings out essential features of

the collected data. This can be done by selecting a suitable number of

classes. Making few classes means over summarization while large number

of the material collected.

OBJECTIVES OF CLASSIFICATION:

1. To condense the mass of data:

Statistical data collected during the course of an investigation

are so varied that it is not possible to appreciate, even after a careful study,

the real significance of the figures, unless they are properly classified small

groups or classes. For example; the huge and fragmented data collected

during a population census has to be classified according to sex, marital

status, education, occupation, etc., to ascertain the structure and nature of the

population.

2. To enable grasping of data:

Unorganized mass of data does not allow a proper grasp of the

definition of statistics (as data) it was indicated that it has to be an

organized mass arranged and classified as per a predetermined mode of

classification.

The figures are easily arranged in a few classes or categories so that

the like go with the like. The data becomes comprehensible when it is sorted

into homogeneous groups as per their respective affinities and cognate

characteristics.

3. To prepare the data for tabulation:

Only classified data can be presented in tabular form.

Classification thus provides a basis for tabulation and further statistical

processing.

4. To study the relationships:

Relation between variable can be established only after the

various characteristics of the data have been known, which is possible only

through classification and tabulation. For example, the characteristics of

income and education can be related but these must first be extracted from

the mass of data.

5. To facilitate comparison:

Classification enables comparison between variables. For

example, the data an households classified on the basis of age, religion,

education, income, expenditure, occupation, etc., can be used for drawing

comparisons between, say, income and education and occupation etc.

Topic: Modes of Classification

TYPES OF CLASSIFICATION

The nature of classification depends upon the purpose and

objective of Investigation. The following are some very common types of

classification.

1. Geographical (or spatial) classification

2. Chronological classification

3. Conditional classification

4. Qualitative classification

5. Quantitative classification

1. Geographical (or spatial) classification

When the data are classified according to geographical location or

region (like states, cities, regions, zones, areas, etc) it is called a

geographical classification. For example, the production of food grains in

India may be presented state-wise in the following manner.

State-wise estimates of production of production of food grains

Sl.No Name of state Total Food

grains

(Thousand

Tones)

1 Andhra Pradesh 1093.90

2 Bihar 12899.89

3 Karnataka 18345.78

4 Punjab 21788.20

5 Uttar Pradesh 41828.30

Geographical classifications are usually listed in alphabetical order for easy

reference. Items may also be listed by size to emphasize the important areas

as in ranking the states by population. Normally, in reference table the first

approach is followed and in summary table the second approach is followed.

2. Chronological classification:

When data are observed over a period of time the type of classification

is known as chronological classification (on the basis of its time of

occurrence). Various time series such as National income figures, annual

output of wheat, monthly expenditure of a household, daily consumption of

milk, etc, are some examples of chronological classification. For example

we may present the figures of population (or production, sales, etc.) as

follows:

Population of India from 1941 to 1991

Sl.No Year Population (in Crores)

1 1941 31.87

2 1951 36.11

3 1961 43.92

4 1971 54.82

5 1981 68.33

3. Qualitative classification:

In qualitative classification data are classified on the basis of some

attribute or quality such as sex, color of hair, literacy, religion, etc. The point

to note in this type of classification is that the attribute under study cannot be

measured, on can only find out whether it is present or absent in the nits of

the population under study. For example it the attribute under study is

population, one can fund out how many persons are living in urban area and

how many in rural area. Thus when only one attribute is studied two classes

are formed is studied two classes are formed, one possessing the attribute

and the other not possessing the attribute. This type of classification is

known as simple classification. For example, the population under study

may be divided into two categories as follows:

In a similar manner, we may classify population on the basis of sex,

i.e., into males and females, or literacy, i.e., into literate and illiterate, and so

on. The type of classification where only two classes are formed is also

called two-fold or dichotomous classification. If instead of forming only two

classes we further divide the data on the basis of some attribute or attributes

so as to form several classes, the classification is manifold classification.

For example , we may first divide the population into males and females on

the basis of the attribute ‘sex’ , each of these classes may be further

Population

Rural

subdivide into ‘literate’ and ‘ illiterate’ on the basis of the attribute ‘literacy’.

Further classification can be made on the basis of some other attribute, say,

employment.

example of manifold classification is given here:

Note: Emp. Indicates Employed and Unemp. Indicates unemployed.

4. Quantitative classification:

Quantitative classification refers to the classification of data according

to some characteristics that can be measured, such as height, weight, income,

sales, profits, production, etc. For example, the students of a college may be

classified according to weight as follows:

Weight (kgs) No of Students

40-50 60

50-60 50

60-70 28

70-80 20

80-90 12

Total 170

Such a distribution is known as empirical frequency distribution or

simple frequency distribution. In this type of classification, there are two

elements, namely 1) the variable, i.e. the weight in the above example, and

2) the frequency, i.e., the number of students in each class.

A frequency distribution refers to data classified on the basis of some

variable that can be measured such as prices, wages, age, number of units

produced or consumed. The term variable refers to the characteristic that

varies in amount or magnitude in a frequency distribution.

A variable may be either continuous or discrete. A continuous variable

also called continuous random variable is capable of manifesting every

conceivable fractional value within the range of possibilities, such as the

height or weight of persons or the weight of person or the weight of the

product. On the other hand, a discrete variable is that which can vary only by

finite “jumps” and cannot manifest every conceivable fractional value. For

instance, the number of rooms in a house e can only take certain values such

as 1,2,3,4 etc. Similarly, the number of machine is and establishments are

discrete variables. Generally speaking, continuous data are derived by

counting. Series which can be described by a continuous variable are called

continuous series. Series represented by a discrete variable are called

discrete series. The following are two examples of discrete and continuous

frequency distributions:

Discrete Continuous

No of children No of families Weight No of persons

0 10 40-50 30

1 40 50-60 50

2 60 60-70 60

3 30 70-80 50

4 15 80-90 40

5 5 90-100 10

Total 160 Total 240

INTRODUCTION TO TABULATION

Meaning and definition of tabulation

Objectives of tabulation

Components of tables

Requirements of good statistical table

Types of tables

General purpose and specific purpose tables

Advantages and disadvantages of classification and tabulation

TABULATION

Topic: meaning and definition of tabulation

MEANING

Although classified data is a step towards simplification and

summarizing of data, it is not able to explain the data fully. Neither does it

analyse the data. Data has to be presented in a suitable form before it can be

studied and its salient features and significance understood. Data can be

presented textually, but it is not an effective form, as matter has to be read

over and over again to grasp the entire range of figures. Presentation of data

involves the use of statistical devices by which classified data are presented

in an understandable form so that data may be quickly grasped. Presentation

of data helps in further statistical treatment and analysis. The main methods

of presenting data are 1) tabulation 2) diagrams and graphs.

Tabulation is a systematic presentation of numerical data in row and

columns. Tabulation of classified data makes it more intelligible and fit for

statistical analysis.

DEFINITION:

According to Tuttle, “A statistical table is the logical listing of

related quantitative data in vertical columns and horizontal rows of numbers,

with sufficient explanatory and qualifying words, phrases and statements in

the form of titles, heading and footnotes to make clear the full meaning of

the data and their origin”.

Topic: Objectives of Tabulation

Presented by: Vivek MN

OBJECTIVES OF TABULATION:

1. To simplify the complex data

Tabulation presents the data set in systematic and concise form

avoiding unnecessary details. The idea is to reduce the bulk of information

(data) under investigation into a simplified and meaningful form.

2. To economize space

By condensing data in a meaningful form, space is saved without

sacrificing the quality and quantity of data.

4. To facilitate comparison

Since table is divided into various parts and for each part tables are

given, the relationship between various items in the tables can be easily

compared.

5. To facilitate statistical analysis

Tabulation is the phase between classification of data and its

presentation. Various statistical technique such as measures of average and

dispersion, correlation and regression, time series, and so on can be applied

to analyse data and then interpreting the results.

6. To save time

From the tabulated data the information can be understood by less

time.

7. To depict trend

Data condensed in the form of table reveal the trend or pattern of

data which otherwise cannot be understood in a descriptive form of

presentation.

8. To help reference

When data are arranged table in a suitable form, they can be easily

identified and can also be used as reference for future needs.

Components Of Table

Presenting data in a tabular form is an art. Statistical table should

contain all the requisite information in a limited space but without any loss

of clarity. Practice varies, but explained below are certain accepted rules for

the construction of an ideal table

1. Table number

A table should be numbered for easy identification and reference in

future. The table number may be given either in the center or side of the

table but above the top of the title of the table. If the number of columns in a

table is large, then these can also be numbered so that easy reference to these

is possible.

2. Title of the table

Every table should be given in a suitable title. Title should be clear,

precise and self explanatory. A complete title must explain in brief and

concise language: (a) what the data are (b) where the data are (c) when the

data occurred (d) how the data are classified

3. Caption (or box head)

Caption refers to the columns headings. It explains what the column

represents. It may consist of one or more columns headings. Under a column

heading there may be subheads. The caption should be clearly defined and

placed at the middle of the column. Caption should be shown in a smaller

letter in order to save space.

4. Stub

Stubs are designation of the rows or row headings. They are at the

extreme left and perform the same function for the horizontal rows of

numbers in the tables as the column heading do for the vertical columns

numbers. The stubs are usually wider than column headings but should be

kept as narrow as possible.

5. Body (or field)

The body of the table contains the numerical information. This is the

most vital part of the table. The collected data are presented in the body of

the table.

6. Head note

It is a brief explanatory statement applying to major part of the

materials in the table. It is used to explain certain points relating to the

whole table that have not been included in the title nor captions or stubs.

Head notes may be used to indicate the units in which the data of the table

are expressed. Head notes should be used only when actually needed. They

may be placed in brackets immediately following the title.

7.Foot note

Anything written below the table is called a foot note. It is written to

further clarify either the title captions or stubs. For example if the data

described in the table pertain to profits earned by a company, then the foot

note may be define whether it is profit before tax or after tax. There are

various ways of identifying foot notes:

a) Numbering foot notes consecutively with smaller number 1, 2,3…..or

letters a, b, c…..or star *, **,……

b) Sometimes symbols like @ or $ are also used to identify foot notes.

7. Source data

The source from where the data contained in the table has been

obtained should be stated. This would help the reader to check the figures

and gather, if necessary, additional information.

A blank model table is given below:

Table Number and Title [Head or Prefatory Note (if any)]

Stub

headings

Caption Total

(rows) Subhead Subhead

Column-head Column Column- head Column head

head

Stub Entries

Total

(columns)

Foot note :

Source note:

Topic: Requirements of good statistical tables

Types of Tables

REQUIREMENTS OF GOOD STATISTICAL TABLES:

“A good Statistical table is not a mere careless grouping of columns and

rows of figures; it is a triumph of ingenuity and technique, a masterpiece of

economy of space combined with a maximum of clearly presented

information. To prepare a good table, one must have a clear idea of the facts

to be presented, the contrasts to be stressed, the points upon which emphasis

is to be placed and lastly a familiarity with the technique of preparation.”

There are no hard and fast rules for preparing a statistical table. However,

commensurate with the objectives and scope of enquiry, the following points

may be come into mind while preparing a good statistical table.

1. Suit the purpose

A table should able to keep the objective of the statistical enquiry.

2. Scientifically prepared

The table should be prepared in a systematic and logically organized

manner, simple and compact so that it is readily comprehensible. It should

be free from all sorts of overlapping and ambiguities.

3. Clarity

A table should be easily understandable, complete and self-

explanatory.

4. Manageable size

A table should be so designed that it is neither very long and narrow

nor very short and broad. If need be, it should be adjusted to the space

provided for the purpose. But such an adjustment should not be at the cost of

legibility. If the space available is inadequate, a table is either split into

various parts or is appended to the report on separate larger-size sheet .If it is

found difficult to accommodate all details into a single table, it is better to

break them down into two or more tables. If too much is incorporated in a

single table, the table will loose its simplicity and understandability

.

5. Columns and rows should be numbered

When there are a number of rows and columns in a table, they must be

numbered for reference.

6. Suitably approximated

If the figures are large, they should be suitably approximated or

rounded. The method rounding should be indicated along with the units of

measurements such as a weight in thousand tones rounded to the nearest

whole number.

7. Attractive get-up

A table should be have an attractive get-up which is appealing to the

eye and mind so the reader grabs it without any strain. The rows and

columns are separated by single, double or thick lines depending on the

broad classes and sub classed used. Related percentages are given close to

corresponding columns and rows. Whereas columns are invariably separated

by lines the rows may or may not be so separated.

8. Units

The units designation should be given at the top of the table below the

title such as ‘price in rupees’ and ‘weight in tones’. If there are different

units for different items then they should be mentioned in respective

columns and rows.

9. Averages and totals

The averages and percentages should as far as possible, be given to the

right or at the bottom of the columns containing original figures. Totals and

sub-totals of both columns and rows and if necessary, the cross totals of each

such group should be given.

10. Logical arrangement of items

There should be logical and systematical classification of items in the

table. Items may be arranged (1) alphabetically, (2) geographically, (3)

chronologically, (4) conventionally (5) in order of magnitude, in ascending

or descending order.

11. Proper lettering

It is not advisable to use too many styles of letters in a table. Large

capitals letters and bold face type may be used for headings, stubs, captions

and small letters may be used for preparatory notes, footnotes and source

notes. Lettering also helps in adjusting the size of the table. Whiling styling

a table, it’s suitably to the user should always be kept in mind. The

expressions should be intelligible. Only accepted common abbreviations

should be used. In case of doubt, a footnote is to be added. The box or circle

may be used to emphasize a figure. If there is gap due to the non-availability

of information, it should be filled by letters N.A., i.e., ’not available’. It is

preferable to avoid the use of dash since a dash can create confusion. The

use of double ditto mark (,,) may be avoided since it can be easily confused

with 11.

Types of tables

Tables can be classified in a number of ways depending on the extent of

coverage given by the survey, objective and scope of the survey, nature of

the survey etc. different types of tables are used. They are given below:

1. Simple and Complex tables.

2. General purpose and special purpose tables.

3. Original and derived table.

1. Simple and Complex tables

The distinction between simple and complex tables are based on the

number of characteristic studied.

In a simple table only one characteristic is shown. Hence this type of

table is also known as one way table. In a complex table. On the other hand

two or more characteristics are shown. Such tables are most popular in

practice because they enable full information to be incorporated and

facilitate a proper consideration of all related facts. When two characteristics

are shown such a table is known as two way table. Or double tabulation.

When three characteristics are shown in a table, this type of tabulation is

known as three way table. When four or more characteristics are

simultaneously shown it is a case of manifold tabulation.

The following examples will illustrate the distinction between simple

and complex table.

S imple table or one-way table

In this type of table only one characteristic is shown. This is simple

type of table. The following is illustration of such a table:

DISTRIBUTION OF POPULATION BY AGE

Age groups

(in years)

Number of persons

(in millions)

0-18

18-40

40-60

60 and above

……

……

……

……

Two-way table:

Such tables are shown two characteristics and formed when either the

stub or the caption is divided into two coordinate parts. The following

example illustrates the nature of such a table:

DISTRIBUTION OF POPULATION BY AGE AND SEX

Age-Groups

(in years)

Number of persons (in millions) Total

Males Females

0-18

18-40

40-60

60 and above

Total

Three-way table

In such a table three characteristics of data are classified. Thus a three

way a table gives us information regarding three inter related characteristics

of a particular phenomenon. For example, the classification of a given

population. With regarding to age, sex and literacy will give rise to three

way table.

DISTRIBUTION OF POPULATION BY AGE, SEX AND LITERACY

AGE

GROUP

(IN

YRS.)

MALES FEMALES TOTAL

Lit

erat

e

illi

tera

te

tota

l

Lit

erat

e

illi

tera

te

tota

l

Lit

erat

e

Illi

tera

te

tota

l

0-18

18-40

40-60

60 and

above

TOTAL

Manifold table

These tables give the information on a large number of inter-related

problems or characteristics of a given phenomenon. These tables are

commonly used in presenting population census data.

Distribution of population by states, age, sex and literacy

STATES

AGE GROUP

(IN YRS.)

MALES FEMALES TOTAL

Lit

erat

e

Illi

tera

te

tota

l

lite

rate

illi

tera

te

tota

l

Lit

erat

e

Illi

tera

te

tota

l

WEST

BENGAL

0-18

18-40

40-60

60 and above

UTTAR

PRADESH

0-18

18-40

40-60

60 and above

TOTAL TOTAL

GENERAL PURPOSE AND SPECIFIC PURPOSE TABLES:

General purpose tables represents the raw data in great detail, covers variety

of information on the same subject and presents the data without any special

analytical purpose. Since they are repository tables. As these tables are

usually placed in the appendix of a report for a reference, they are

sometimes called reference tables. Reference tables contain ungrouped data,

basic for a particular report, usually containing a large amount of data and

frequently related to a tabular appendix.

Tables published by various government agencies like CSO, Reserve

Bank of India etc. are such tables. The sole purpose of such table is to

present detailed statistical information pertaining to national income,

population, employment, prices, production, money supply, taxation etc on a

continuing basis.

A special purpose table also known as text table, summery table, or

analytical table presents data relating to a specific problem. For example

tables prepared by a firm for managerial decision present data on a specific

issue desired by the management. Further, a table presenting data related to

the sale of a particular product should be termed specific purpose table.

“These tables are those in which have been analyzed, but rather the

results of analysis”. Such tables are usually smaller than reference table and

are generally found in the body of a report. These tables can be arranged to

emphasize the relationship between various characteristics of data or to

facilitate comparisons between specific problems relating to enquiry.

Original and derivative tables :

Original tables are also known as classification tables, contain data

which were initially collected from the original source. But a table which

presents results derived from the original data like averages, coefficients etc.

would constitute derivative table. Similarly, a time series forms a table

containing original values but a table containing trend values constitutes a

derived table. Quite often original data and the derived results like

percentages of the total, mean, standard deviations etc, are presented in the

form of a table.

Topic:

General purpose table:

The general purpose table is also called as reference table. This

general purpose table is mainly used for facilitating easy reference of the

collected data. This type of table presents the data in such a manner that the

individual items are readily found by the reader. This type of table is formed

without any specific objectives. But this general purpose table contains large

mass of data.

Special purpose table:

The other names for this special purpose tables are text table and

summery table. The main objective of this type of table is to present the data

pertaining to a specific problem. This table is generally smaller in size as

compared to the general purpose tables. The specific purpose tables are

generally formed to highlight the relationship between various

characteristics or to facilitate their on.

Advantages of classification and tabulation

1. Clarifies the object

The information arranged in the form of table is easily accessible and

provides adequate and very clear information to the user. There is no need to

search for the required information in the table and the table gives the ready

information.

2. Simplifies the complex data

The main objective of the tabulation is to reduce the mass i.e. the size

of the data and present the data in the simplest possible way. The idea is to

make a complex data more intelligible and meaningful. While presenting the

data in tables all the complexities are removed and the data is made very

simple and clear.

3. Economic space

The economies of space are achieved without sacrificing the quality

and usefulness of the data. Repetition of explanatory terms and phrases can

be avoided in tabulation.

4. Facilitates the comparison

It facilitates the quick comparison of the statistical data shown in

rows and column. Comparable figures are put in highlighted column to grab

more attention.

5. It helps in references

The tabulated information is convenient to refer to and identify at

any future data. With mechanized tabulation there is permanent storage and

the facility to tabulate in different forms to suit the needs of business.

6. Depict the trend

Tabulated data is easily amenable to statistical calculation of trend and other

features of data.

Disadvantages of tabulation and classification

1. Complicated process

Some time the arrangement of data into rows and columns become

complicated if the person arranging or tabulating does not have the required

knowledge.

2. Every data cannot be put into tables

Some data’s can be put into tabular form but not all the data’s. S we

cannot arrange all the given data in the tabular form or it will be very

difficult to put every data into the tabular form.

3. Lack of flexibility

Once the tale is created then we can not make changes regularly. If

we want to make changes then we should change the whole table.