Tabulation & Graphical Representation Of Data

Submitted by: Neeraja.R

TABULATION

Tabulation refers to the systematic arrangement of the information in rows and columns. It is a function of arranging the data in an orderly manner through the table. In simple words, tabulation is a layout of figures in rectangular form with appropriate headings to explain different rows and columns. The main purpose of the table is to simplify the presentation and facilitate comparisons.

OBJECTS & IMPORTANCE OF TABULATION

Tabulation is a technique to present and interpret the complex information in a simple and systematic form. The main objectives of the process of tabulation are as follows:

The main purpose is to simplify the complex information so that it can be easily understood.

Under tabulation, data is divided into various parts and for each part there are totals and sub-totals. Therefore the relationship between parts can be easily known.

Since data are arranged in a table with title and a number it is easy to identify and use for the required purposes.

It briefs the data which therefore becomes easy to present the data in form of graph.

It makes complex data simple which becomes easy to understand the data. Tabulation makes easy to analyse the data from table.

RULES OF TABULATION

There are no hard & fast rules for tabulation of data but for constructing good table, the following general rules should be observed while tabulating statistical data.

First of all, there should be a proper title to each table. Table number and title should be written above the table.

The table should suit the size of the paper; therefore the width of the column should be decided before hand.

Number of columns and rows should neither be too large nor too small. Captions, headings and sub-headings of the rows and columns must be self-

explanatory. Each column and row should be given title. The title of the column is called

the caption and the title of the row is called the stub. As far as possible, the figures should be approximated before tabulation to

reduce unnecessary details. Items should be arranged alphabetical or chronological or geographical order

or accordingly to size. Units of measurement under each heading or sub-heading must always be

indicated. The total and sub-total of items of the table must be written. Ditto marks should not be used in a table because sometimes it creates

confusion. Table should be simple and attractive.

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PARTS OF A TABLE

TABLE NUMBERWhen there are more than one table, each table must have a number. The

tables are numbered in a sequence so that they may be easily referred to. The number of the table should be written at the middle on the top of the table.

TITLEA table should have suitable title which is placed at the top in bold letters. The

title describes the contents of the table briefly. As far as possible, the title should be complete and unambiguous as regards the subject matter of the data. It should be clear, properly worded and self-explanatory. Long titles cannot be read as promptly as short titles, but they may have to be used for the sake of clarity when necessary. In such a situation, a “catch title” may be given above the main title.

CAPTIONSThey refer to the heading of the information shown at the top of the vertical

columns. Captions generally give the basis of classification eg., sex, meters, occupation, etc. Under the captions, there may be sub-headings. They are written in small letters along with units if any.

STUBSThey refer to the headings of the information shown at the extreme left of the

horizontal rows. They perform the similar function as that performed by the captions. Captions and stubs are interchangeable.

BODYIt refers to the numerical information that is presented in captions and stubs. It

is the most important part of the table which describes the entire data attractively and precisely. It covers the major portion of the table. The table must contain sub-totals of each separate class of data and grand total for the combined classes.

HEAD NOTEIt is a brief note given below the title normally in brackets which clarifies the

contents of the table. It gives an explanation concerning the entire table or main parts of it, eg the units of measurement are usually expressed in a head note as ‘in hectare’, ‘in million’, ‘in quintets’, etc.

FOOT NOTEIt is a brief note given at the foot of the table. Foot notes are meant to clarify

certain terms in detail. They may be attached to any part of the table by using the asterisk (*) to show the explanation is given below.

SOURCEThe source is given in case of secondary data. It gives the sources from which

the data were obtained. The source should give the name of the publication and journal or periodical, page number, table number, etc from which the data have been collected.

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LIMITATIONS OF TABULATION

Tabulation suffers from the following limitations: Tables contain only numerical data; they do not contain details. Qualitative expressions are not possible through tables. Tables can be used by experts to draw conclusions. Common men do not

understand them properly.

UNIVARIANT TABLE

Sl. No. Description Nos.

1 Male 100

2 Female 300

Total 400

BIVARIANT TABLE

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Sl. No.

DescriptionSkilled worker

Unskilled worker

Nos.

1 Male 50 50 100

2 Female 150 150 300

Total 400

DIAGRAMMATIC & GRAPHICAL REPRESENATION OF DATA

Besides the tabular form, the data may also be presented in some graphical or diagrammatic form.

The transformation of data through usual methods like graphs, diagrams, maps and charts is called graphical representation of data.

NEED FOR DIAGRAMATIC & GRAPHICAL REPRESENTATION

It gives an attractive and effective impression due to the usual impression of data rather than that of the tabulated figures.

It saves time which is otherwise needed in drawing inferences from the non-graphical form.

The entire data are visible at a glance. These make it easy to understand the patterns of population growth,

distribution and density, sex ratio, age-sex composition, occupational structure, etc.

The graphical method of representation of data enhances our understanding.

GENERAL RULES FOR DRAWING GRAPHS & DIAGRAMS

1. SELECTION OF A SUITABLE GRAPHICAL / DIAGRAMMATICAL METHOD

Each characteristic of the data can only be suitable represented by an appropriate method.Example:

To show the data related to the temperature or growth of population between different periods of time line graphs are used.

Similarly, bar diagrams are used for showing rainfall or production of commodities.

Population distribution, both human and livestock, or the distribution of the crop producing area are shown by dot maps.

Thus, it is necessary and important to select suitable graphical method to represent data.

2. SELECTION OF SUITABLE SCALE

Each diagram or map is drawn to a scale which is used to measure the data. The scale must cover the entire data that is to be represented. The scale should neither be too large nor too small.

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3. DESIGN

The diagram or map should have following design:

I. TITLEThe title of the diagram or map must be clear and should

include:The name of the areaReference year of the data used &The caption of the diagram

These are written with different font sizes and thickness. The title, subtitle and corresponding year is shown in the centre at the top of map or diagram.

II. INDEXThe index must clearly explain the colours, shades, symbols

and signs used in the map and diagram. Index is shown either at the lower left or lower right side of the map sheet.

III. DIRECTIONThe map should show the direction North and properly placed

on the top.

TYPES OF DIAGRAMS

1. ONE DIMENSIONAL DIAGRAMSa) Bar diagram

2. TWO DIMENSIONAL DIAGRAMSb) Pie diagram

3. PICTOGRAMS4. CARTOGRAMS (MAPOGRAMS)

ONE DIMENSIONAL DIAGRAMS – BAR DIAGRAMS

There only one dimension of the figure is taken into account. Bars are drawn with different widths and lengths. There are different types of bar diagrams such as:

1) Line Diagram2) Simple Bar Diagram3) Multiple Bar diagram4) Subdivided Bar Diagram5) Derivation Bars6) Duo-directional Bars &7) Paired Bars

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LINE DIAGRAMS

These diagrams are used when there is large number of values of variable with variations in their values within a small range. They are in form of vertical lines relating to respective values of variable. A proper space should be left uniformly in between the two lines. The line diagrams are most suitable for the comparative study related items.

Example:

DIAGRAM SHOWING PROFITS OF FIRMS

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Profits (Rs. In Lakhs) No. of Firms5 35

10 8015 2020 3025 5030 6835 9040 4045 2550 10

SIMPLE BAR DIAGRAMS

These diagrams can be drawn either vertically or horizontally. The bars must have the similar width and uniform space should be kept between the two bars. The values and variables are taken either in ascending order or in descending order. Time series and other series are generally represented in the simple bar diagram. We can use different colour or shades or dots for each bar if necessary to identify the data and to make the diagram attractive.

Example: Following data is about the raw materials exported by a country

Raw Materials Import in Crores

Aluminum 65

Copper 50

Iron 100

Silver 10

DIAGRAM SHOWING IMPORT OF RAW MATERIALS BY COUNTRY ‘A’

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MULTIPLE BAR DIAGRAMS

These diagrams are also known as “compound bar diagrams”. They are adopted when two or more phenomena over a number of years are compared with each other. Similar attributes in each period are presented for the purpose of comparison. Different colours or shades or dots are used for each attribute in each set of period. An index is prepared to identify different attributes.

Example: Following data gives the working population of men, women and children during the year 1997 in 3 states.

Population Men Women Children

Karnataka 3900000 2500000 1800000

Andhra 4500000 3000000 2000000

Maharashtra 5000000 3800000 2200000

DIAGRAM SHOWING WORKING POPULATION IN 3 STATES DURING THE YEAR 1997

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SUB-DIVIDED BAR DIAGRAMS

These diagrams are also known “components bar diagrams”. Each bar is sub-divided according to the components consisting in it. A given magnitude of the phenomenon can be broken into parts of which it is composed. Each bar, the different portions are made from of the bar to distinguish components. The complete bar represents the total values of variable along with the various values of components. Each component can be distinguished by using different colours or shades or dots.

Example: Data of number of students in two colleges in different departments

College Arts Science Commerce AgricultureA 1200 800 600 400B 700 500 600 200

The above data is to be converted into cumulative for showing the different components and their break-up.

College Arts A+S A+S+ C Arts+S+C+AgriA 1200 800 600 400B 700 500 600 200

DIAGRAM SHOWING STUDENTS IN TWO COLLEGES IN DIFFERENT DEPARTMENTS

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DEVIATION BARS

These bars depict the net deviations in different values. The positive deviation is taken above the ‘OX’ axis and the negative deviations taken below it. The two phenomenon ‘Profit & Losses’, favourable balance of trade or unfavourable balance of trade and surplus of deficit are depicted by deviation bar diagrams.

They are also called ‘Bilateral Bar Diagrams’.

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TWO DIMENSIONAL DIAGRAMS

PIE DIAGRAM / CHARTA pie chart is a circle graph divided into pieces, each displaying the

size of some related pieces of information. Pie charts are used to display the sizes of parts that make up some whole. There are 360 degrees at the centre of a circle. Taking the data equal to 360 degrees, the proportionate sector is cut representing the different attributes of the same data. Pie chart is obtained by dividing the circle into corresponding degrees of angles and then by representing the sub-sets of the data. Hence, it is also called as divided circle diagram. The angle of each variable is calculated using the following formula. X * 360 --------- where X is the variable N N is the total of all variables If the data is given in percentage form the angles are collected using the given formula: Percentage of X * 360 --------------------------- 100Example: Following data is the expenditure of family A.

Items of Expenditure Expenditure in Rs.Food 540Rent 180

Clothing 180Education 90Lighting 40

Miscellaneous 40Saving 10

DIAGRAM SHOWING EXPENDITUREOF FAMILY A IN Rs.

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PICTOGRAMS

Pictogram is a device of picture by which the data can be presented. Pictures are used for comparing statistical data. To convert the dull data into an interesting and attractive view through objects of daily observation, the image of the entire data is fixed in the picture. Relationship between figures and their comparison can be studied with the help of pictograms easily.

The number of pictures drawn or the size of the pictures should be proportional to the values of the different magnitudes to be presented to the values of the different magnitudes to be presented. A symbol must represent a general concept which can be understood clearly and easily. A symbol should be neither be too small nor too large.Example: Mode of transportation people using.

Mode of Transportation ValuesTrains 175Cars 250Ships 425

Planes 225TOTAL 1075

DIAGRAM SHOWING PEOPLE USING DIFFERENT MODES OF TRANSPORT

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CARTOGRAMS

Instead of using pictures, different types of maps are used to present the data. Maps represent the regional data like languages spoken, religion belonging, rainfall in a region, weather report, etc. On a map, the data are shown with different colours, shades, dots or points having different attributes.

DIAGRAM SHOING THE POPULATION OF INDIA IN THE YEAR 2001

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GRAHPS

There are different types of graphs such as:1. Line graph2. Histogram3. Frequency Polygon4. Ogive Curves

LINE GRAPHS

A line graph is a way to summarise how two pieces of information are related and how they vary depending on one another. The numbers along a side of the line graph is called the scale.

Example: Following is the weight of Mr. John in kgs. in different years.

Year Weight of John (in Kgs.)1991 681992 701993 741994 741995 73

GRAPH SHOWING WEIGHT OF JOHN

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HISTOGRAM

Histogram is a device of graphic representation of a frequency distribution. It is constructed by electing a set of rectangles on each class-interval on the horizontal respective frequencies. Frequencies are shown on Y axis and the height of rectangle represents the frequency of the respective interval. The area of all rectangles joined together represents the total frequencies.

Example:Marks No. of Students62- 67 467-72 872-77 1277-82 1682-87 2487-92 2092-97 4

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FREQUENCY POLYGON

Frequency polygon is a device of graphic representation of a frequency distribution. It is a simple method of drawing the graph with the help of histogram. The histogram is first constructed, then the mid-points of the top of all rectangles by straight lines. This is done under the assumption that the frequencies in each class interval are evenly distributed.

The area of the frequency polygon is equal to the area of the histogram, as the area left outside is geometrically equal to the area included in it.

This is especially good at showing the form or shape of the distribution. It is often the method of choice when two or more distributions are to be compared.

Example:Marks No. of Students62- 67 467-72 872-77 1277-82 1682-87 2487-92 2092-97 4

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OGIVE CURVES

Ogive curve is a graphic presentation of cumulative frequency distribution of a continuous series. It is best used when you want to display the total at any given time.

Example: savings of company A in the different months

Month Savings (in dollars) CFJanuary 300 300February 100 400

March 100 500April 300 800May 100 900June 100 1000Total 1000

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