Presentation of Data - National Council Of Educational ... · PDF filegenerally three forms of...

Presentation of Data

1. INTRODUCTION

You have already learnt in previouschapters how data are collected andorganised. As data are generallyvoluminous, they need to be put in acompact and presentable form. Thischapter deals with presentation of dataprecisely so that the voluminous datacollected could be made usable readilyand are easily comprehended. There aregenerally three forms of presentation ofdata:

• Textual or Descriptive presentation• Tabular presentation• Diagrammatic presentation.

2. TEXTUAL PRESENTATION OF DATA

In textual presentation, data aredescribed within the text. When thequantity of data is not too large this formof presentation is more suitable. Lookat the following cases:

Case 1

In a bandh call given on 08 September2005 protesting the hike in prices ofpetrol and diesel, 5 petrol pumps werefound open and 17 were closed whereas2 schools were closed and remaining 9schools were found open in a town ofBihar.

Studying this chapter shouldenable you to:• present data using tables;• represent data using appropriate

diagrams.

CHAPTER

© NCERT

not to

be re

publi

shed

PRESENTATION OF DATA 4 1

Case 2

Census of India 2001 reported thatIndian population had risen to 102crore of which only 49 crore werefemales against 53 crore males. 74 crorepeople resided in rural India and only28 crore lived in towns or cities. Whilethere were 62 crore non-workerpopulation against 40 crore workers inthe entire country, urban populationhad an even higher share of non-workers (19 crores) against the workers(9 crores) as compared to the ruralpopulation where there were 31 croreworkers out of a 74 crore population....

In both the cases data have beenpresented only in the text. A seriousdrawback of this method of presentationis that one has to go through thecomplete text of presentation forcomprehension but at the same time, itenables one to emphasise certain pointsof the presentation.

3. TABULAR PRESENTATION OF DATA

In a tabular presentation, data arepresented in rows (read horizontally)and columns (read vertically). Forexample see Table 4.1 below tabulatinginformation about literacy rates. It has

3 rows (for male, female and total) and3 columns (for urban, rural and total).It is called a 3 × 3 Table giving 9 itemsof information in 9 boxes called the"cells" of the Table. Each cell givesinformation that relates an attribute ofgender ("male", "female" or total) with anumber (literacy percentages of ruralpeople, urban people and total). Themost important advantage of tabulationis that it organises data for furtherstatistical treatment and decision-making. Classification used intabulation is of four kinds:

• Qualitative• Quantitative• Temporal and• Spatial

Qualitative classification

When classification is done accordingto qualitative characteristics like socialstatus, physical status, nationality, etc.,it is called qualitative classification. Forexample, in Table 4.1 the characteris-tics for classification are sex andlocation which are qualitative in nature.

TABLE 4.1Literacy in Bihar by sex and location (per cent)

Location TotalSex Rural Urban

Male 57.70 80.80 60.32Female 30.03 63.30 33.57

Total 44.42 72.71 47.53

Source: Census of India 2001, ProvisionalPopulation Totals.

Quantitative classification

In quantitative classification, the dataare classified on the basis of

© NCERT

not to

be re

publi

shed

4 2 STATISTICS FOR ECONOMICS

characteristics which are quantitativein nature. In other words thesecharacteristics can be measuredquantitatively. For example, age, height,production, income, etc are quantitativecharacteristics. Classes are formed byassigning limits called class limits forthe values of the characteristic underconsideration. An example ofquantitative classification is Table 4.2.

TABLE 4.2Distribution of 542 respondents by

their age in an election study in Bihar

Age group No. of(yrs) respondents Per cent

20–30 3 0.5530–40 61 11.2540–50 132 24.3550–60 153 28.2460–70 140 25.8370–80 51 9.4180–90 2 0.37

All 542 100.00

Source: Assembly election Patna centralconstituency 2005, A.N. Sinha Institute of SocialStudies, Patna.

Here classifying characteristic is age

in years and is quantifiable.

Activities

• Construct a table presentingdata on preferential liking of thestudents of your class for Star

News, Zee News, BBC World,CNN, Aaj Tak and DD News.

• Prepare a table of(i) heights (in cm) and(ii) weights (in kg) of students

of your class.

Temporal classification

In this classification time becomes theclassifying variable and data arecategorised according to time. Timemay be in hours, days, weeks, months,years, etc. For example, see Table 4.3.

TABLE 4.3Yearly sales of a tea shop

from 1995 to 2000

Years Sale (Rs in lakhs)

1995 79.21996 81.31997 82.41998 80.51999 100.22000 91.2

Data Source: Unpublished data.

In this table the classifyingcharacteristic is year and takes valuesin the scale of time.

Activity

• Go to your library and collectdata on the number of books ineconomics, the library had atthe end of the year for the lastten years and present the datain a table.

Spatial classification

When classification is done in such away that place becomes the classifyingvariable, it is called spatialclassification. The place may be avillage/town, block, district, state,country, etc.

Here the classifying characteristic iscountry of the world. Table 4.4 is anexample of spatial classification.

© NCERT

not to

be re

publi

shed


TABLE 4.4Export from India to rest of the world inone year as share of total export (per cent)

Destination Export share

USA 21.8Germany 5.6Other EU 14.7U K 5.7Japan 4.9Russia 2.1Other East Europe 0.6OPEC 10.5Asia 19.0Other LDCs 5.6Others 9.5

All 100.0

(Total Exports: US $ 33658.5 million)

Activity

• Construct a table presentingdata collected from students ofyour class according to theirnative states/residentiallocality.

4. TABULATION OF DATA AND PARTS OF

A TABLE

To construct a table it is important tolearn first what are the parts of a goodstatistical table. When put together ina systematically ordered manner theseparts form a table. The most simple wayof conceptualising a table may be datapresented in rows and columnsalongwith some explanatory notes.Tabulation can be done using one-way, two-way or three-wayclassification depending upon thenumber of characteristics involved. Agood table should essentially have thefollowing:

(i) Table Number

Table number is assigned to a table foridentification purpose. If more than onetable is presented, it is the tablenumber that distinguishes one tablefrom another. It is given at the top orat the beginning of the title of the table.Generally, table numbers are wholenumbers in ascending order if there aremany tables in a book. Subscriptednumbers like 1.2, 3.1, etc. are also inuse for identifying the table accordingto its location. For example, Tablenumber 4.5 may read as fifth tableof the fourth chapter and so on.(See Table 4.5)

(ii) Title

The title of a table narrates about thecontents of the table. It has to be veryclear, brief and carefully worded so thatthe interpretations made from the tableare clear and free from any ambiguity.It finds place at the head of the tablesucceeding the table number or justbelow it. (See Table 4.5).

(iii) Captions or Column Headings

At the top of each column in a table acolumn designation is given to explainfigures of the column. This iscalled caption or column heading.(See Table 4.5)

(iv) Stubs or Row Headings

Like a caption or column heading eachrow of the table has to be given aheading. The designations of the rowsare also called stubs or stub items, andthe complete left column is known as

© NCERT

not to

be re

publi

shed


stub column. A brief description of therow headings may also be given at theleft hand top in the table. (See Table4.5).

(v) Body of the Table

Body of a table is the main part and itcontains the actual data. Location ofany one figure/data in the table is fixedand determined by the row and columnof the table. For example, data in thesecond row and fourth column indicatethat 25 crore females in rural India

were non-workers in 2001. (See Table4.5).

(vi) Unit of Measurement

The unit of measurement of the figuresin the table (actual data) should alwaysbe stated alongwith the title if the unitdoes not change throughout the table.If different units are there for rows orcolumns of the table, these units mustbe stated alongwith ‘stubs’ or‘captions’. If figures are large, theyshould be rounded up and the method

(Note : Table 4.5 presents the same data in tabular form already presented through case 2 intextual presentation of data)

Table 4.5 Population of India according to workers and non-workers by gender and location

Location Gender Workers Non-worker TotalMain Marginal Total

Male 17 3 20 18 38Female 6 5 11 25 36Total 23 8 31 43 74



Source : Census of India 2001

Foot note : Figures are rounded to nearest crore

All

Urb

anRu

ral

Bod

y of

the

tabl

e←

Footnote↑

Source note↑

Row

Hea

ding

s/st

ubs

→

↑Units

(Crore)

↓Column Headings/Captions

↓Title

↓Table Number

© NCERT

not to

be re

publi

shed


of rounding should be indicated (SeeTable 4.5).

(vii) Source Note

It is a brief statement or phraseindicating the source of data presentedin the table. If more than one source isthere, all the sources are to be writtenin the source note. Source note isgenerally written at the bottom of thetable. (See Table 4.5).

(viii)Footnote

Footnote is the last part of the table.Footnote explains the specific featureof the data content of the table which isnot self explanatory and has not beenexplained earlier.

Activities

• How many rows and columnsare essentially required to forma table?

• Can the column/row headingsof a table be quantitative?

5. DIAGRAMMATIC PRESENTATION OF

D A T A

This is the third method of presentingdata. This method provides thequickest understanding of the actualsituation to be explained by data incomparison to tabular or textualpresentations. Diagrammatic presenta-tion of data translates quite effectivelythe highly abstract ideas contained innumbers into more concrete and easilycomprehensible form.

Diagrams may be less accurate butare much more effective than tables inpresenting the data.

There are various kinds of diagramsin common use. Amongst them theimportant ones are the following:

(i) Geometric diagram(ii) Frequency diagram(iii) Arithmetic line graph

Geometric Diagram

Bar diagram and pie diagram come inthe category of geometric diagram forpresentation of data. The bar diagramsare of three types – simple, multiple andcomponent bar diagrams.

Bar Diagram

Simple Bar Diagram

Bar diagram comprises a group ofequispaced and equiwidth rectangularbars for each class or category of data.Height or length of the bar reads themagnitude of data. The lower end of thebar touches the base line such that theheight of a bar starts from the zero unit.Bars of a bar diagram can be visuallycompared by their relative height andaccordingly data are comprehendedquickly. Data for this can be offrequency or non-frequency type. Innon-frequency type data a particularcharacteristic, say production, yield,population, etc. at various points oftime or of different states are noted andcorresponding bars are made of therespective heights according to thevalues of the characteristic to constructthe diagram. The values of thecharacteristics (measured or counted)

© NCERT

not to

be re

publi

shed


retain the identity of each value. Figure4.1 is an example of a bar diagram.

Activity

• You had constructed a tablepresenting the data about thestudents of your class. Draw abar diagram for the same table.

Different types of data may requiredifferent modes of diagrammaticalrepresentation. Bar diagrams aresuitable both for frequency type andnon-frequency type variables andattributes. Discrete variables like familysize, spots on a dice, grades in anexamination, etc. and attributes suchas gender, religion, caste, country, etc.can be represented by bar diagrams.Bar diagrams are more convenient fornon-frequency data such as income-

expenditure profile, export/importsover the years, etc.

A category that has a longer bar(literacy of Kerala) than anothercategory (literacy of West Bengal), hasmore of the measured (or enumerated)characteristics than the other. Bars(also called columns) are usually usedin time series data (food grainproduced between 1980–2000,decadal variation in work participation

TABLE 4.6Literacy Rates of Major States of India

2001 1991

Major Indian States Person Male Female Person Male Female

Andhra Pradesh (AP) 60.5 70.3 50.4 44.1 55.1 32.7Assam (AS) 63.3 71.3 54.6 52.9 61.9 43.0Bihar (BR) 47.0 59.7 33.1 37.5 51.4 22.0Jharkhand (JH) 53.6 67.3 38.9 41.4 55.8 31.0Gujarat (GJ) 69.1 79.7 57.8 61.3 73.1 48.6Haryana (HR) 67.9 78.5 55.7 55.8 69.1 40.4Karnataka (KA) 66.6 76.1 56.9 56.0 67.3 44.3Kerala (KE) 90.9 94.2 87.7 89.8 93.6 86.2Madhya Pradesh (MP) 63.7 76.1 50.3 44.7 58.5 29.4Chhattisgarh (CH) 64.7 77.4 51.9 42.9 58.1 27.5Maharashtra (MR) 76.9 86.0 67.0 64.9 76.6 52.3Orissa (OR) 63.1 75.3 50.5 49.1 63.1 34.7Punjab (PB) 69.7 75.2 63.4 58.5 65.7 50.4Rajasthan (RJ) 60.4 75.7 43.9 38.6 55.0 20.4Tamil Nadu (TN) 73.5 82.4 64.4 62.7 73.7 51.3Uttar Pradesh (UP) 56.3 68.8 42.2 40.7 54.8 24.4Uttaranchal (UT) 71.6 83.3 59.6 57.8 72.9 41.7West Bengal (WB) 68.6 77.0 59.6 57.7 67.8 46.6India 64.8 75.3 53.7 52.2 64.1 39.3

© NCERT

not to

be re

publi

shed


Fig. 4.1: Bar diagram showing literacy rates (person) of major states of India, 2001.

rate, registered unemployed over theyears, literacy rates, etc.) (Fig 4.2).

Bar diagrams can have differentforms such as multiple bar diagramand component bar diagram.

Activities

• How many states (among themajor states of India) hadhigher female literacy rate thanthe national average in 2001?

• Has the gap between maximumand minimum female literacyrates over the states in twoconsecutive census years 2001and 1991 declined?

Multiple Bar Diagram

Multiple bar diagrams (Fig.4.2) areused for comparing two or more sets ofdata, for example income andexpenditure or import and export for

different years, marks obtained indifferent subjects in different classes,etc.

Component Bar Diagram

Component bar diagrams or charts(Fig.4.3), also called sub-diagrams, arevery useful in comparing the sizes ofdifferent component parts (the elementsor parts which a thing is made up of)and also for throwing light on therelationship among these integral parts.For example, sales proceeds fromdifferent products, expenditure patternin a typical Indian family (componentsbeing food, rent, medicine, education,power, etc.), budget outlay for receiptsand expenditures, components oflabour force, population etc.Component bar diagrams are usuallyshaded or coloured suitably.

© NCERT

not to

be re

publi

shed


TABLE 4.7Enrolment by gender at schools (per cent)of children aged 6–14 years in a district of

Bihar

Enrolled Out of schoolGender (per cent) (per cent)

Boy 91.5 8.5Girl 58.6 41.4All 78.0 22.0

Data Source: Unpublished data

A component bar diagram showsthe bar and its sub-divisions into twoor more components. For example, thebar might show the total population ofchildren in the age-group of 6–14 years.The components show the proportionof those who are enrolled and thosewho are not. A component bar diagrammight also contain different componentbars for boys, girls and the total ofchildren in the given age group range,as shown in Figure 4.3. To construct acomponent bar diagram, first of all, abar is constructed on the x-axis with

its height equivalent to the total valueof the bar [for per cent data the barheight is of 100 units (Figure 4.3)].Otherwise the height is equated to totalvalue of the bar and proportionalheights of the components are workedout using unitary method. Smallercomponents are given priority inparting the bar.

Pie Diagram

A pie diagram is also a component

Fig. 4.2: Multiple bar (column) diagram showing female literacy rates over two census years 1991and 2001 by major states of India.

Interpretation: It can be very easily derived from Figure 4.2 that female literacy rate over the yearswas on increase throughout the country. Similar other interpretations can be made from the figurelike the state of Rajasthan experienced the sharpest rise in female literacy, etc.

Fig. 4.3: Enrolment at primary level in a districtof Bihar (Component Bar Diagram)

© NCERT

not to

be re

publi

shed


diagram, but unlike a component bardiagram, a circle whose area isproportionally divided among thecomponents (Fig.4.4) it represents. It

is also called a pie chart. The circle isdivided into as many parts as there arecomponents by drawing straight linesfrom the centre to the circumference.

Pie charts usually are not drawnwith absolute values of a category. Thevalues of each category are firstexpressed as percentage of the totalvalue of all the categories. A circle in apie chart, irrespective of its value ofradius, is thought of having 100 equalparts of 3.6° (360°/100) each. To findout the angle, the component shallsubtend at the centre of the circle, eachpercentage figure of every componentis multiplied by 3.6°. An example of thisconversion of percentages ofcomponents into angular componentsof the circle is shown in Table 4.8.

It may be interesting to note thatdata represented by a component bardiagram can also be representedequally well by a pie chart, the onlyrequirement being that absolute values

of the components have to be convertedinto percentages before they can beused for a pie diagram.

TABLE 4.8 Distribution of Indian population by their

working status (crore)

Status Population Per cent AngularComponent

Marginal Worker 9 8.8 32°Main Worker 31 30.4 109°Non-Worker 62 60.8 219°

All 102 100.0 360°

Fig. 4.4: Pie diagram for different categories ofIndian population according to working status2001.

Activities

• Represent data presentedthrough Figure 4.4 by acomponent bar diagram.

• Does the area of a pie have anybearing on total value of thedata to be represented by thepie diagram?

Frequency Diagram

Data in the form of grouped frequencydistributions are generally representedby frequency diagrams like histogram,frequency polygon, frequency curveand ogive.

© NCERT

not to

be re

publi

shed


Histogram

A histogram is a two dimensionaldiagram. It is a set of rectangles withbases as the intervals between classboundaries (along X-axis) and withareas proportional to the classfrequency (Fig.4.5). If the class intervalsare of equal width, which they generallyare, the area of the rectangles areproportional to their respectivefrequencies. However, in some type ofdata, it is convenient, at timesnecessary, to use varying width of classintervals. For example, when tabulatingdeaths by age at death, it would be verymeaningful as well as useful too to havevery short age intervals (0, 1, 2, ..., yrs/0, 7, 28, ..., days) at the beginningwhen death rates are very highcompared to deaths at most otherhigher age segments of the population.For graphical representation of suchdata, height for area of a rectangle isthe quotient of height (here frequency)and base (here width of the classinterval). When intervals are equal, thatis, when all rectangles have the samebase, area can conveniently berepresented by the frequency of anyinterval for purposes of comparison.When bases vary in their width, theheights of rectangles are to be adjustedto yield comparable measurements.The answer in such a situation isfrequency density (class frequencydivided by width of the class interval)

instead of absolute frequency.

TABLE 4.9Distribution of daily wage earners in a

locality of a town

Daily No. Cumulative Frequenceyearning of wage 'Less than' 'More than'(Rs) earners (f)

45–49 2 2 8550–54 3 5 8355–59 5 10 8060–64 3 13 7565–69 6 19 7270–74 7 26 6675–79 12 38 5980–84 13 51 4785–89 9 60 3490–94 7 67 2595–99 6 73 18100–104 4 77 12105–109 2 79 8110–114 3 82 6115–119 3 85 3

Source: Unpublished data

Since histograms are rectangles, a lineparallel to the base line and of the samemagnitude is to be drawn at a verticaldistance equal to frequency (orfrequency density) of the class interval.A histogram is never drawn for adiscrete variable/data. Since in aninterval or ratio scale the lower classboundary of a class interval fuses withthe upper class boundary of theprevious interval, equal or unequal, therectangles are all adjacent and there isno open space between two consecutiverectangles. If the classes are notcontinuous they are first converted intocontinuous classes as discussed inChapter 3. Sometimes the commonportion between two adjacentrectangles (Fig.4.6) is omitted giving abetter impression of continuity. Theresulting figure gives the impression ofa double staircase.

© NCERT

not to

be re

publi

shed


A histogram looks similar to a bardiagram. But there are more differencesthan similarities between the two thanit may appear at the first impression.The spacing and the width or the areaof bars are all arbitrary. It is the heightand not the width or the area of the barthat really matters. A single vertical linecould have served the same purposeas a bar of same width. Moreover, inhistogram no space is left in betweentwo rectangles, but in a bar diagramsome space must be left betweenconsecutive bars (except in multiplebar or component bar diagram).Although the bars have the samewidth, the width of a bar is unimportantfor the purpose of comparison. Thewidth in a histogram is as importantas its height. We can have a bardiagram both for discrete and

continuous variables, but histogram isdrawn only for a continuous variable.Histogram also gives value of mode ofthe frequency distribution graphicallyas shown in Figure 4.5 and the x-coordinate of the dotted vertical linegives the mode.

Frequency Polygon

A frequency polygon is a planebounded by straight lines, usually fouror more lines. Frequency polygon is analternative to histogram and is alsoderived from histogram itself. Afrequency polygon can be fitted to ahistogram for studying the shape of thecurve. The simplest method of drawinga frequency polygon is to join themidpoints of the topside of theconsecutive rectangles of thehistogram. It leaves us with the two

Fig. 4.5: Histogram for the distribution of 85 daily wage earners in a locality of a town.

© NCERT

not to

be re

publi

shed


ends away from the base line, denyingthe calculation of the area under thecurve. The solution is to join the twoend-points thus obtained to the baseline at the mid-values of the two classeswith zero frequency immediately ateach end of the distribution. Brokenlines or dots may join the two ends withthe base line. Now the total area underthe curve, like the area in thehistogram, represents the totalfrequency or sample size.

Frequency polygon is the mostcommon method of presenting groupedfrequency distribution. Both classboundaries and class-marks can beused along the X-axis, the distancesbetween two consecutive class marksbeing proportional/equal to the widthof the class intervals. Plotting of databecomes easier if the class-marks fallon the heavy lines of the graph paper.

No matter whether class boundaries ormidpoints are used in the X-axis,frequencies (as ordinates) are alwaysplotted against the mid-point of classintervals. When all the points have beenplotted in the graph, they are carefullyjoined by a series of short straight lines.Broken lines join midpoints of twointervals, one in the beginning and theother at the end, with the two ends ofthe plotted curve (Fig.4.6). Whencomparing two or more distributionsplotted on the same axes, frequencypolygon is likely to be more useful sincethe vertical and horizontal lines of twoor more distributions may coincide ina histogram.

Frequency Curve

The frequency curve is obtained bydrawing a smooth freehand curvepassing through the points of the

Fig. 4.6: Frequency polygon drawn for the data given in Table 4.9

© NCERT

not to

be re

publi

shed


frequency polygon as closely aspossible. It may not necessarily passthrough all the points of the frequencypolygon but it passes through them asclosely as possible (Fig. 4.7).

Ogive

Ogive is also called cumulativefrequency curve. As there are two typesof cumulative frequencies, for exampleless than type and more than type,accordingly there are two ogives for anygrouped frequency distribution data.Here in place of simple frequencies asin the case of frequency polygon,cumulative frequencies are plottedalong y-axis against class limits of thefrequency distribution. For less thanogive the cumulative frequencies areplotted against the respective upperlimits of the class intervals whereas formore than ogives the cumulative

frequencies are plotted against therespective lower limits of the classinterval. An interesting feature of thetwo ogives together is that theirintersection point gives the medianFig. 4.8 (b) of the frequency distribu-tion. As the shapes of the two ogivessuggest, less than ogive is neverdecreasing and more than ogive isnever increasing.

TABLE 4.10Frequency distribution of marks

obtained in mathematics

Marks Number of ‘Less than’ ‘More than’students cumulative cumulative

x f frequency frequency

0–20 6 6 6420–40 5 11 5840–60 33 44 5360–80 14 58 2080–100 6 64 6

Total 64

Fig. 4.7: Frequency curve for Table 4.9

© NCERT

not to

be re

publi

shed


Arithmetic Line Graph

An arithmetic line graph is also calledtime series graph and is a method ofdiagrammatic presentation of data. Init, time (hour, day/date, week, month,year, etc.) is plotted along x-axis andthe value of the variable (time seriesdata) along y-axis. A line graph byjoining these plotted points, thus,obtained is called arithmetic line graph(time series graph). It helps inunderstanding the trend, periodicity,etc. in a long term time series data.

Activity

• Can the ogive be helpful inlocating the partition values ofthe distribution it represents?Fig. 4.8(b): ‘Less than’ and ‘More than’ ogive

for data given in Table 4.10

Fig. 4.8(a): 'Less than' and 'More than' ogive for data given in Table 4.10

© NCERT

not to

be re

publi

shed


Fig. 4.9: Arithmetic line graph for time series data given in Table 4.11

TABLE 4.11Value of Exports and Imports of India

(Rs in 100 crores)

Year Exports Imports

1977–78 54 601978–79 57 681979–80 64 911980–81 67 1251982–83 88 1431983–84 98 1581984–85 117 1711985–86 109 1971986–87 125 2011987–88 157 2221988–89 202 2821989–90 277 3531990–91 326 4321991–92 440 4791992–93 532 6341993–94 698 7311994–95 827 9001995–96 1064 12271996–97 1186 13691997–98 1301 15421998–99 1416 1761

Here you can see from Fig. 4.9 thatfor the period 1978 to 1999, althoughthe imports were more than the exportsall through, the rate of accelerationwent on increasing after 1988–89 andthe gap between the two (imports andexports) was widened after 1995.

6. CONCLUSION

By now you must have been able tolearn how collected data could bepresented using various forms ofpresentation — textual, tabular anddiagrammatic. You are now also ableto make an appropriate choice of theform of data presentation as well as thetype of diagram to be used for a givenset of data. Thus you can makepresentation of data meaningful,comprehensive and purposeful.

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Val

ues

(in

Rs

100 C

rore

s)

Scale: 1cm=200 crores on Y-axis

ExportsImports

Year

© NCERT

not to

be re

publi

shed


Recap• Data (even voluminous data) speak meaningfully through

presentation.• For small data (quantity) textual presentation serves the purpose

better.• For large quantity of data tabular presentation helps in

accommodating any volume of data for one or more variables.• Tabulated data can be presented through diagrams which enable

quicker comprehension of the facts presented otherwise.

EXERCISES

Answer the following questions, 1 to 10, choosing the correct answer1. Bar diagram is a

(i) one-dimensional diagram(ii) two-dimensional diagram(iii) diagram with no dimension(iv) none of the above

2. Data represented through a histogram can help in finding graphically the(i) mean(ii) mode(iii) median(iv) all the above

3. Ogives can be helpful in locating graphically the(i) mode(ii) mean(iii) median(iv) none of the above

4. Data represented through arithmetic line graph help in understanding(i) long term trend(ii) cyclicity in data(iii) seasonality in data(iv) all the above

5. Width of bars in a bar diagram need not be equal (True/False).

6. Width of rectangles in a histogram should essentially be equal (True/False).

7. Histogram can only be formed with continuous classification of data(True/False).

© NCERT

not to

be re

publi

shed


8. Histogram and column diagram are the same method of presentation ofdata. (True/False).

9. Mode of a frequency distribution can be known graphically with thehelp of histogram. (True/False).

10. Median of a frequency distribution cannot be known from the ogives.(True/False).

11. What kind of diagrams are more effective in representing the following?(i) Monthly rainfall in a year(ii) Composition of the population of Delhi by religion(iii) Components of cost in a factory

12. Suppose you want to emphasise the increase in the share of urbannon-workers and lower level of urbanisation in India as shown inExample 4.2. How would you do it in the tabular form?

13. How does the procedure of drawing a histogram differ when classintervals are unequal in comparison to equal class intervals in afrequency table?

14. The Indian Sugar Mills Association reported that, ‘Sugar productionduring the first fortnight of December 2001 was about 3,87,000 tonnes,as against 3,78,000 tonnes during the same fortnight last year (2000).The off-take of sugar from factories during the first fortnight of December2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnesfor exports as against 1,54,000 tonnes for internal consumption andnil for exports during the same fortnight last season.’(i) Present the data in tabular form.(ii) Suppose you were to present these data in diagrammatic form which

of the diagrams would you use and why?(iii) Present these data diagrammatically.

15. The following table shows the estimated sectoral real growth rates(percentage change over the previous year) in GDP at factor cost.

Year Agriculture and allied sectors Industry Services(1) (2) (3) (4)

1994–95 5.0 9.2 7.01995–96 –0.9 11.8 10.31996–97 9.6 6.0 7.11997–98 –1.9 5.9 9.01998–99 7.2 4.0 8.31999–2000 0.8 6.9 8.2

Represent the data as multiple time series graphs.

© NCERT

not to

be re

publi

shed

Presentation of Data - National Council Of Educational ... · PDF filegenerally three forms of...

Documents

Transcript of Presentation of Data - National Council Of Educational ... · PDF filegenerally three forms of...