L-6 PRESENTATION OF STATISTICAL DATA

8/7/2019 L-6 PRESENTATION OF STATISTICAL DATA

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6.PRESENTATION OF STATISTICAL DATA I

6.1 INTRODUCTIONIn t h e previous lesson. you have learnt about the methods of organising..'ncl condensing!data in the form of arrays and ffequency distributions. It is first step towards analysislofdata. Another step inthis direction ispresentation of data to highlight and compare significan:statistical facts.Generally data are presented inthe fonn of tables and graphs or charts. A table is a systematicorganisation of data in columns and rows. There are various types of graphs. In this lessonyou will learn about table. bar charts, pie diagram (or chart) and time series line graph.6.2 OBJECTIVESAfter going through this lesson you will be able to :

explain the meaning ~nd purpose of a table;distinguish between reference table a n d special purpose table;draw the format of a table;explain the meaning and construction of simple and multiple bar charts;explain the need and construction of component barcharts;explain the meaning of pie chart and .steps inits construction;explain the meaning of a time series graph and steps in it s construction.

6 . 3 TABLE(a) MeaningA table is a systematic arrangement of related statistical data in columns and rows with


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Presentation of Statistica I 0 0 1 1 : 1 :;6$ ',.

ome predetermined aim or purpose. Can you arrange the following information in tabular.0

There are 50 science and 50 arts students in a college. The number of students from poormilies is same for each course and their total is 30. Whereas science and commerceourses are equally populru: in rich families; yet the number of rich arts student is twice asuch. In a1140 students are from the rich families studying in the college. The majorityoftudents are from middle class families and their number is 80."

us arrange this information in tabular form. There are 150 students in all. A table leavesmore lasting impression on human mind than statements saying the same thing.

Table 6.1Distribution of students according to course and economic status

Science Arts Commerce TotalRich 10 2 0 10 40Middle Class 30 20 30 80Poor 10 10 10 30Total 50 50 50 150

b) Purposehe purpose of a tab~e is to simplify 'presentation of related d~a and make comparisonsasy. The reader can easily locate the desired information. For example, the purpose ofbh;"6.2 might beta show the imports and exports of coon try 'A' vis-a-vis other countries,C,D and E.

Tabl~6.2Imports and Exports of Country 'A' during 1995-96 (Rs. Crores)Country Imports Exports

(1) (2) (3)B 8 0 70C 65 700 40 42E 1 0 8

rom the-table 6.2 on exports and imports, we can easily locate the country which hasighest exports. The data given in rows is read from left to right. for example. row 1 showsat country A imports 80 from B and exports 70 to. B. The data given in column is readrom above to downwards. For example, column 2 shows that country A imports 80, 65, 40nd 10 respectively from countries B, C. D and E.


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:: Econom ics

(c) Types of TablesBasically we have two types of tables (i) Reference or general purpose tables or(ii) specialpurpose or text tables. Let us discuss them one by one.

(i)Reference or general purpose tables: These tables are in a way a store of informationwith an aim of presenting detailed statistical material, From these tables we can derivesmaller tables. Generally, statistical tables presented byGovernment ofIndia and its variousstatistical agencies and departments ar~ reference or general purpose tables.(ii) Special purpose or text tables: These tables are smaller and can b e obtained fromreference tables. They aim to analyse a particular aspect so that we are able to bring out aspecific point or answer a specific question.(d) Partsofa TableParts (or elements) ofa table vary from table to table depending upon the nature of data andpurpose of a table. However, some points are common to all (see format of table 6.3). Theyare:

Table 6.3( Title ,. )

(in Rs. crores)Stub Head

Subcolumnhead

Subcolumnhead

Sub columnhead

Sub columnhead

Column head I Column head 2

Stub Entries Main Body o f the Table(field)FootnoteSource of data ( )( " )(1) Table Number:If more than one table/has been used or presented at one place. it is always better to givethem serial numbers.,' It makes further reference to them easy. This number is alwaysindicated in the centre at the top.(2) Title:Title is to the table what heading is to an essay. Itappears at the top of a table and giveidea about what is contained in the main body of the table. The title should be brief and tthe point. It is better if the title is presented in bold letters or capital letters.


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Presentation of Statistical Data - 6 7- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - ~ -

(3) Head note (or prefatory note) :Itis written below the title. Itclarifies the contents of the table and unit o f measurement like"in rupees crores" or "in lakh tons" or "in thousand bales of cotton" etc. Itmust be writtenin brackets on right side (top) ofthe table immediately below the title. For example, in table6.1 the unit of measurement is rupees crores.(4) Stub : "'~.The stub consists of stub head and stub entries. Whereas stubdescribes the stub entriesdown below it, each stub entry labels a given data placed in its row. Both stub head and stubentries appear on the left hand column ofthe table. Further, stub entries describe the columnheads.(5) Main Body or Field :It is the most important part of the table and contains the numerical information about whicha hint is given in the title. For example, if the title is "Exportsand Imports of Country Aduring 1995-96", it clearly shows that the body of the table contains statistical/numericalinformation on value of exports and imports of country A with different countries.(6) Footnote:Itis a qualifying statement placed at the bottom ofa table. Its purpose is to explain omissionor lim itations of the data presented in main body of the table. For example, if t he data for thevear is not available then at the bottom of a table it is mentioned there.

A table is a systematic presentation of data in columns and rows.A table can be general purpose (reference) or special purpose (text).Each table has certain essential parts like table number, title, head note, caption,stub (stub head and stub entries), main body (field), footnote and source.

(7) Source of Data :Last but not the least, it is essential to mention thesource of data presented in the table. Ithelps the reader to check the original source of data himself and get more of it on thesubject. Itshould mention infonnation like title. edition, p ag e number and so u rce of publicationetc.POINTS TO REMEMBER

IN T EX T QUES TION S 6 .11. State whether the following statements are true or false:a) Satisfactory collection of data must be followed by its good presentation.b) Tabulation is the only way of presenting data.c) Tables help in intelligent use ofstatistical data.d) The title of a table should be brief and to the point.


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~8::Econom ics

2. Fill in the blanks using suitable word given in the bracket.a) A .. is a systematic arrangement of statistical data in columns and rows.(table, graph)b) Head note is written below the ................. of the table. (title.footnote)c) The consists of stub head and stub entries ..d) A foot-note is placed at the . 1 of a table.

(stub, note)(top, main body, bottom)

6.4 BARCHARTSORDIAGRAMSMeaningA bar can be defined as a thick 'line', 'Often made thicker to draw attention of the reader.The heightofthis bar shows the quantity ~fthe variable we want to present. Itis also calledone dimensional diagram because only height of'the b a r is important and its base orwidth isnot taken into account. To make them look more beautiful, bars are either -coloured orshaded in different ways. .Types of bar charts:There are two types of bar charts (a) simple and (b) components.(a) Simple bar cbarts :'-.Simple bar charts can be (i) Single bar charts, and (ii) Multiple bar charts.(i) Single bar cbarts : We can either have vertical bars (figure 6J) or horizontal bars(figure 6.2). Normally vertical bars are often used. Let us now explain how a bar diagramcan h e prepared from a given data in table 6.4.

Table 6.4Number of can registered in

three States

Cars registered in states


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Presentation of Statistical Data :~9 ._ I:

se) is raised according to the value ofvariable (here the number of cars

gistered), For example, rectangleresenting State A is raised upto 8,000,State B upto 10,000 and for Sute C'4,000. (Set). figure 6.1)

Cars registered in statesNo , of c ars regi stered in three states . . .~~~~~Q~~~Qo 00QQQQQQQo 0000.~00Q0QQQQQ00000 0

\\

case we prefer to. use horizontal-bars,represent States on Ysaxis. Here the ..(rectangles) are drawn horizontally8,000, 10.000 and 4,000 cars

pecti ve Iyfor the three States A, Band(See figure 6.2)

~.

Fig. 6.2 : Single Bar Chart

Multiple bar charts: .metimes it is desired to. represent more than one interrelated series data on a b ar diagram.such cases also simple bar diagram is not suitable. We have to use what is known asultiple bar diagram. Here the number of bars fo r each year or region or zone is equal to'enumber ofvariables (data) to be represented. For example, imports and exports will bepresented by two bars; selling price, cost price and profits by three bars and so on.rmally we do not take more than three bars because it becomes complicated. The methoddrawing bars is same as explained for simple bar diaWks. Two samples of multiple baragrams are presented below (figure 6.3 based on table 6.5 and figure 6.4 based on Table

Table .6.5Imports and Exports of Country 'X' during 1990-95(Rs. crores)

Year Imports Exports1 9 9 0 500 4501 9 9 1 52 0 48 01992 6 O Q . 5 0 01993 .~ 6~O 6 2 01994 786 7001995 800 7 2 0


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-j.tJ.:: Economics

Imports and Exports of Country 'X' during 1990-95. n0 : : : 80 0. .,u 700. . .0. . 600{;>

_ 5 500 L ~ U. . . . . . 400. . .1: : 3000Q. 2 0 0> o! IU 1 0 0"0!: 0


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Presentation of Statistical Data ;:71.

(b) Component bar charts : .A simple bar diagram explained above is used to present only one variable. But when abreakdown of'total or a series of'totals is to b e represented, we have to use what is calledsub-divided or component bar diagrams. For example, we may like to represent trend insales of Super Bazar in a big city like Delhi for (say) three years divided into four zones--North, East. West and South. Here we use sub-divided or component b a r diagram as shownin figure 6.S.lt is based on imaginary (or hypothetical) data shown in table 6.7.

Table 6.7Zone-wise Trends in Sales of Super Bazar

.Area Sales (in takh Rs.)1995 1996 1997

North zone 1 00 . 15 0 20 0East zone 80 14 0 1 40West zone 300 320 320South zone 1 2 0 1 4 0 2 4 0Tota1 6 0 0 750 9 0 0

9 0 0800700- -< I i 600=.c : 50 0. . : . . :.s 400.S 3 0 0._,

fI)0 200jjjVJ 100

0

South zo~

Zone-wise trends in sales of Super Bazar

.North tone

1995 1996Year

1997

lig. 65 : Component Bar ChartSteps inthe construction of a component bar diagramStep 1. Measure sales on Y axis and year on X axis and place them in a box type diagramas show n in figure 6.5.


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Presentation of Statistical Data: :fTable 6.8

Monthly Family Budget of the Industrial Worker of Bombay

Items Expenditure Tota l Degree = Value of items' group x 3600percentage . Total value360 60Food 360 x 100=60 - x3600 216.0600 100J08 18Clothing 1 08 xloo=18 - x3600 64.8600 100.,90 15Housing 60 x100",,15 - x3600 54.0600 10024 4Comforts 24 x100=4 - X 3600 14.4600 l O O12 x100=2 2Education & 1 2 - ~360O 7.2"entertainment 600 1006 IMisc. 6 x100=1 - x 360 = 3.6100 100

Total 6 0 0 1 0 0 3600

Housing 15%

60%Food

Education and Entertainment2%

Misc. 1%

Clothing1 8%

Comforts

Fig. 6.6 : Pie Diagram


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jft-:: Economics

POINTS TO REMEMBER

A bar diagram is often defined as a thick line made thicker to draw attention ofthe viewer or reader. Bars can be drawn horizontally or vertically. Height of abar diagram shows value of the variable. Its base has no value. That is why it iscalled one dimensional.A s against a simple 'bar diagram. where only one variable can be presented. wehave what is called sub-divided or component bar diagram where two or morerelated variables can be presented.A pie diagram is a circle sub-di vided into components to present the proportionof different constituent parts of the totah.For different components, proportionsare presented in terms of degrees obtained by the formula.D f 11 Value of the component/group x 3.600egree, or a componen group = ToW of all components/groups

1.a)b)c)

State whether the following statements are true or false ;The width of a bar diagram is important.In bar diagram, height of bars shows the value of the variable.We can have vertical as well as horizontal bars to present some data having onevariable.When a break down of data is to be represented we use multiple bar diagram.d)

2 .a)

Fill in the blanks with suitable word out of those given in the brackets :A pie chart is also called diagram. (a bar, an angular. amultiple bar)Value of the component x 3600 _ .T tal f II t - (area, radius, degree for a component)o 0 a componen sb)

6 . 6 TIME SERIES LINE GRAPHStatistical data can also be presented in the form of line graphs. A line graph records therelationship between two variables. Ifone of the two variables is time-days, weeks, monthsor years-we get a time series line graph. For example.Jet' us draw a line graph on the basisof the following data on production of crude oil in country 'X' from 199D~91to 1995-96.

Table 6.9Production ,of Crude on inCountry 'X'

Year PrOduction(in lakh tonnes)

1990-911991921992-931993-941994-951995-96

1 0 616221 126 029 0302


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Presentation of Statistical Data ::75

3 5 0 . 13 0 0 t2 5 0 I2 0 0

150 tI100 A

5 0 t -o ~ -+-----.-t---.-.- ...,.-~-__I1990-91 1991-92 1992-93 1993-94 1994-95 1995-96

The above graph is a time series line graph. The time is represented, on the X axis and theproduction on the Y axis. Time and production ar e two variables in this graph. It is theproduction which changes with time. In other words as time passes production is affectedand it increases or decreases or may remain constant. Since production changes with time,it is said to be dependent on time. Production is, therefore, treated as a dependent variable.Time is not influenced by production and therefore taken as an independent variable .. .

Yearfig. 6.7 : 'lime Series Line Graph

Point A on the line graph (also called curve) shows that production of crude oil in country'X' in the year 1990-91 was 102lakh tonnes. Similarly points B,C,D,E and F show productionlevels in the subsequent years. The upward rising of the curve from left to right indicatesthat production of crude oil in Country 'X' is constantly rising since 1990-91.It is possible to show two or more comparable dependent variables on a time series linegraph. In that case each dependent variable will be recorded on a separate: curve. Forexample. take the following data on exports and imports of country 'X'.

Table 6.10Exports and Imports of country 'X'

Year Imports(in Rs. 100 crores)

Exports(in Rs. 100 crores)

1990-911991-921992-931993-941994-951995-96

677 88 8e n

1 19110

1 2 51 3 61431 5 81721 9 8


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,76 : Economics

The time series line graph prepared on the basis of above data is given below (see figu6.8). .

.hnports"_ ..- .an1001 m140l I D100II)00402)O+-----~----~----_+--~--~--~1QD.91 19t1-B:!, 1~ro 19B-94 1ffi4.95 1~

. . ..iI- .~..~..~.", . .. . . . . .. . . . . . . '"Exports

YearFig. 6.8 : Time Series Line Graph

In the above graph imports are shown in broken line and exports otherwise. Suchpresentation is very useful to make comparison between two dependent variables.POINTS TO REMEMBER

A line graph shows relationship between two variables. If one of the twovariables is time, we get a time series line graph.

In a time series line graph. time is independent variable and represented on Xaxis. The other variable is dependent variable shown on the Y axis.

Two or more comparable dependent variables can be shown on a time series " H n e g ra p h.

INtEXT Q t J E S T I O N S 6 .3Fill in the blanks :a) A ....................... graph shows the relationship between two variables.b) Ifone of the variable on a line graph is it is called time series line graph.c) In a time series line graph .is an independent variable.d) In a time series line graph variable is represented on the Y axis.


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Presentation of StatisticalData : :77

ACIlVlTY

1. Make a blank table (format) showing the distribution of students of 12th class accordingto :a) Subject groups i.e. Science, Arts and Commerceb) Sex i.e. boys and girls

2. Thefollowing table gives selling price and cost price of a good 'X' for five years.Year 1990 1991 1992 1993 , \1 294\

Selling price of 'X' 105 110 120 90 160Cost price O f 'X' 100 80 1 2 0 1 2 0 1 4 0

Plot the aboveinfonnation on a graph paper in the form of line graph. What type of graphsdo you get ?WHATYOUHA VE LEARNf

After data havebeen collected, they must now be arranged and presented insome useful form.

A good presentation highlights the data and brings out important points fornecessary comparison.

Tables, frequency arrays, frequency distribution, time series line graphs etc.,are some important ways in which data are presented.

A table is a systematic presentation of data in columns and rows. Each table has some essential constituent parts like table number, title, head, '. note, caption, stubs, main body, foot note and source of information.

A graph is also an important way of presenting data-such as time series linegraphs, bar charts, pie diagrams etc.

When an economic variable is presented with time, it is called a time series linegraph.

A bar diagram is defined as a thick line made thicker to draw attention of theviewer. Its height is important as it shows the value of the variable. A bar diagram can be drawn either vertically or horizontally. When a breakdown of a tota1 or a series of totals is to be shown, we use what

is known as sub-divided or component bar diagram. A pie diagram is also an important and effective way of presenting data. It is a

circle sub-divided into components to present the proportion of differentconstituent parts of the total.


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18 Economics

TERMINAL EXERCISE1. What is a statistical table? List its various parts.2. What is the purpose of preparing a table? Inthis context distinguish between refer

table and text table.3. What is a bar chart? Explain briefly its various types.4. What is the difference between simple bar diagram. sub-divided or component

diagram and multiple bar diagram? "5. Explain themeaning an d uses of a pie diagram. Prepare a pie diagram of fa

expenditure from the following data :S.Na. Items EXpenditure < R S . )1. Food 4802 . Clothing 3003 . Education and Entertainment 3 3 04 . Rent 4505 . Miscellaneous 2 4 0

Total EXpenditure 18006. Explain the meaning of time series line graph with the help of an example.7. Draw a time series line graph on the basis of following data~~\ __

Production of Cement inCountry 'X'Year Production

(in lakh tonnes)1990-911991-921992-931993-941994-951995-96

68788161789 5


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Presentation of Statistical Data :~9;r

text Questi9n 6.11. (a) True (b) False (c) True (d) True2. (a) table (b) title (e) Stub. (d) bottom

text Questions 6.21. (a) False (b) True (c) True (d) False2. (a) an angular (b) degree for a component

text QuestionS 6.3(a) line (b) time (c) time (d) dependent

rm\na1 Exercise1. Read section 6.3 (a) and 1 )2. Read section 6.3 (b) an d (e)3 . Read section 6.4

. 4. Read section 6.45. Read section6.56. Read section 6.67. Read section6.6

Subject group _ _ _ _ ~ -- _ _ ---- -T rn ruBoys Girls

idelines to Activities1. Hint:Number o f S tu den ts

ScienceArtsCommerceTotala) Fill up yourself. the title, footnote. etc. i. e. parts of a table.b) Fill up the main body of the table with imaginary figures.

2. (a)Measure year on X axis and selling price (S.P.) as well as cost price (C.P.)on Y axis. W e get tim e series line graph.

L-6 PRESENTATION OF STATISTICAL DATA

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