Q. 1. What do you mean by statistics? Give its characteristics.

Ans. Statistics is concerned With scientific methods for collecting, organizing Summarizing, presenting and analysing data, as well as drawing valid conclusions and making reasonable decision the basis of such analysis. In a narrow sense, the term is used to denote that data themselves or number derived from the data as for example averages.

Statistics are aggregates and facts affected to a marked extent by multiplicity of causes numerically expressed enumered or estimated according to reasonable standards of accuracy, in a systematic manner for a predetermined purpose and placed in relation to each other,”

–Horace Secrist

Characteristics of Statistics : Statistics should possess the following characteristics :

1. Statistics are concerned with “population of facts rather with a single fact”. A single age, height or sale does not constitute statistics. A series or mass of accidents, sales or ages forni statistics and they may be studied in relation to time, place and number of occurrences with the help of statistical methods.
2. Statistics are affected to a marked extent by a multiplicity of causes. This Incan that statistics production is attributable to a number of factors viz, rainfall, soil, fertility, quality of seeds, methods of cultivation etc. All these factors acting jointly determine the amount of the yield and it is not possible for anyone to assess the individual contribution of any one of these factors.
3. Statistics must be numerically expressed, enumered or estimated. Statistical method apply
only to data which are capable ofbeing reduced to quantitative forms. Qualitative expression such as beauty, health intelligence care not statistics unless a numerical equivalent is assigned to each expression, e.g., intelligence can be quantified by assigning certain scores to some subjects of study and nothing down the marks obtained by the students.
4. Statistics must be enumerated or estimated according to reasonable standards of accuracy. This mean that if aggregates of numerical facts are called statistics they must be reasonable accurate.This is necessary because statatical data are to serve as a basis for statistical investigation. If the basis happens to be incorrect. The result are bound to be misleading. It must however be clearly understood, that it is not mathematical accuracy, but only reasonable accuracy, that is necessary in statistical work
5. Statistics should be collected in a systematic manner for a predetermined purpose. The statistical method to be applied depend on the purpose of enquiry, which must be determined before the enquiry begins. In the absence of a predetermined purpose the data will be useless.
6. Statistics should be placed in relation to each other. Numerical facts may be placed in relation

Q. 2. What is statistical thinking?

Ans. Statistical thinking is a form of logical thinking and is a part of our daily lives. When we say that something or somebody is typical, we are thinking in terms of statistical averages, and departure from type is statistical variation. When we generalise from a few cases to a very large number, we are using sampling methods. A conclusion that two things always go together involves a pattern of found in statistical correlation. When we mention the cost of living has gone up by 20 per cent in a certain period, we are thinking of index number. Hence, statistical thinking is not alien to everyday thinking, but is a scientific form of it.

“The statistical approach though universal in its underlying ideas, must be tailored to fit the peculiarities of each concrete problem to which it is applied. It is dangerous to apply statistics in cook book style, using the same recipes over and over, without careful study of the ingredients of each new problem.”

Q. 3. Describe the functions and importance of statistics. (2017)

Ans. The functions of statistics are as follows :

1. To Present Facts in a Definite Form : Without a statistical study our ideas are likely to be vague, indefinite and hazy, but figures help us to represent things in their true perspective. Thus
facts are presented in a definite and unambiguous form. For instance, the statements that some
students out of 100, who had appeared for a certain examination, were declared successful would not give as much information as the one the 94 students out of 100 who took the examination were declared successful.

2. To Simplify Unwieldy and Colette Data so as to Make them Understandable : It is not an easy job to treat large numbers and hence they are simplified either by taking a few figures to serve as a representative sample or by taking average to give a bird’s eye view of the large masses. For instance, the data may be- condensed in the form of a table, graph or diagram or through an average, ratios or rates.

3. Statistics is a Technique of Making Comparisons : Once the data are simplified, they can be correlated and compared. The relationship between two different groups is best represented by certain mathematical quantities, such as averages, coefficients, rates and ratios.

4. Statistics Helps in correlating data : Correlation in statistics means how changes in one phenomenon or variable lead to changes in another phenomenon or variable. For example, greater rainfall should normally lead to greater agricultural production; greater wages should lead to greater productivity; greater price should lead to lesser demand but greater supply, and so on. Statistics helps to study such inter-dependent changes with the help of correlation analysis. Besides, it describes and analyses, in definite terms, the direction of change and the nature and degree of association between different inter-dependent phenomena or variables.

5. Statistics Formulates and Tests Hypothesis : Different hypotheses or laws in all fields of human effort can be formulated and tested with the help of statistics. Whether it is the effect of space travel on human body, or the speed of a planet, or the effect of a medicine, or the effect of price rise on the demand of a product, statistics must be used.

6. statistics Helps in Framing Policies : Statistics aids government and the business to frame policies to pursue their objectives and goals since it summarises and analyses data and thus helps in forecasting. Suppose the government wants the per capital income to grow so that weaker sections of the society get the maximum benefit, statistics will come to its aid.

Q. 4. Give the advantages of diagrammatic and graphic presentation of data.

Ans. Advantages of Diagrammatic and Graphic Presentation of Data : Diagrammatic and graphic presentation has a number of advantage some of which are enumerated below :

I. Diagrams and graphs are visual aids which give a bird’s eye view to a given set of numerical
data.

2, Diagrams are generally more attractive and leave a more lasting impression on the mind as
compared to the dry and un-interesting statistical figures.

3. They are more eye catching.

4, They save lot of time as very little effort is required to grasp them and draw meaningful
inferences from them,

5. When properly constructed, diagrams and graphs readily show information that might otherwise be lost amid the details of numerical tabulations. They highlight the salient features of the collected data facilitate comparisons among two or more sets of data and enable us to study the relationship between them more readily.

6. Graphs reveal the trends, if any, present in the data more widely than the tabulated numerical figures and also exhibit the way in which the trend changes.

Q. 5. What are the basic differences between diagrams and graphs?

Ans. Difference between Diagrams and Graphs : Though there is no clear-cut line of demarcation between the two, yet following points of difference may be noted :

1. For constructing a graph we generally make use of graph paper whereas a diagram is generally constructed on a plain paper. In other words, a graph represents mathematical relationship (though not necessarily functional) between two variables whereas a diagrams does not.

2. Diagrams are more attractive to the eye and as such are better suited for publicity and propaganda. They do not add anything to the meaning of the data and therefore from the point of view of a statistician or research worker they are not helpful in analysis. Graphs, on the other hand, are very much used by the statistician and the research worker in analysis.

3. For representing frequency distributions and time series, graphs are more appropriate than diagrams. In fact, for presenting frequency distributions diagrams are rarely used.

Q. 6. What is frequency polygon? Explain in brief.

Ans. A frequency polygon is another graphical representation of a frequency distribution in the form of a polygon superimposed on a histogram by joining with straight lines the mid-points of the top of the adjacent rectangles. The two end-points are also joined to the x-axis at the mid-point’s of the empty classes at each end of the frequency distribution. In a frequency polygon so constructed the area of the polygon is the same as that of a histogram. A frequency polygon, superimposed on histogram, for the data in table ahead is given in fig. (a). A frequency polygon can also be drawn by joining the successive plotted points whose abscissae (distances along with x-axis) represent the mid-points of the classes and ordinates (distances along with y-axis) represent the corresponding class frequencies. In table the mid-points of the classes are 24.5, 34.5, 74.5 and 84.5 with corresponding frequencies 4,6, 7 and 4 respectively. Thus, for drawing a frequency polygon, we first mark the points (x) with coordinates (24.5, 4) (34.5, 6) (74.5, 7) and (84.5, 4) respectively, The marked points are then joined by straight lines as shown in fig. (b). The end points, however, are still joined with x-axis at the mid points of the empty classes (14.5 and 94.5) at each end of the distribution as we did in fig. (a).

In fig. (b), one observes that the first point (14.5) located on x-axis is a bit away from the origin O. In some distributions, this starting class or point may be farther away from the origin making it difficult to accommodate the rest of the classes or points on the x-axis with a suitable scale of measurement. Fors locating classes or points away from origin, we may use a break in x-axis. The break, represented as (f f), indicates that the y-axis z has been moved towards the starting point on x-axis for conveniently representing all the classes or points on this axis. The concept will be more clear from the fig. (b). representing the frequency polygon for the frequency distribution in table.

The main object of drawing a frequency polygon is to get a continuous frequency curve so that it may provide an idea about the shape of the frequency distribution.

Q. 7 Statistics is the science of counting”. Discuss. (2016)

Ans. Science refers to a systematised body of knowledge. It studies cause and effect relationship and attempts to make generalisation in the form of scientific principles of laws. It describes objectively and avoids vague judgements as good or bad. Like other sciences, statistical methods are also used to answer the questions like. How an investigation should be conducted? In what way the valid and reliable conclusions can be drawn? How far these conclusions are dependable? Hence» statistics is a science. The science of statistics is different from Physics, Chemistry etc, Statistics is called the science of scientific methods. That is why some statisticians do not consider it a pure science but a scientific method. In the words of Croxton and Cowden, “As science, the statistical method is apart of the general scientific method and is based on the same fundamental ideas and processes”.

Q. 1. Discuss the importance, limitations and scope of statistics.
or Define statics and discuss its scope and limitations.
or Describe the importance of statistics.

Ans. Statistics is concerned With scientific methods for collecting, organizing Summarizing presenting and analysing data, as well as drawing valid conclusions and making reasonable decision number derived from the data as for example averages.

“Statistics are aggregates and facts affected to a marked extent by multiplicity of causes numerically expressed enumered or estimated according to reasonable standards of collected in a systematic manner for a predetermined purpose and placed in relation to each other,”                             —Horace Secrist

Importance of Statistics

Today it is impossible for the Government to function without collecting a vast amount of information, partly as a by-product of its normal administration and more particularly for specific needs of national economic planning. Government today are the biggest consumers as well as producers of statistics. Legislation, whether it is on labour or minimum wages for agricultural workers, about divorce or dowry, out smuggling, about foreign exchange regulations and so on,
requires a sound statistical base for objective assessment and effective tackling of these problems, Even on the most elementary level, it is impossible to understand psychology, education, sociology, economics, business management, finance or physical sciences, without some general idea of the meaning of an average, of variation, of sampling, of how to interpret tables and graphs.

The basic concepts of statistics are the same in all fields; however, these concepts are emphasised and utilised somewhat differently in each of the branches of knowledge. Despite the fact that statistics performs some very important functions in collecting and analysing facts regarding social and economic problems, it is not without limitations.

### Limitations of Statistics

Its limitations are follows :

1. Statistics does not Study Individuals : An individual figure, howsoever important it may be cannot become of a part of a statistics study. For example, the marks secured by Himanshu in an can t examination will not be studied in statistics, even if he has topped in the examination because it is an individual item. It is the marks secured by a group of students that would constitute statistics and be studied.

2. Statistics does not study Qualitative Aspects : Statistics studies only those aspects of human or social behaviour that can be expressed in numbers. 3.    Statistical Results are True only in General and on an Average : Statistical laws are not exact laws like mathematica ,chemical on physical laws. They are derived by taking a majority of cases and not true for every individual. 4.    Statistics can be Misused by Ignorant or Wrongly Motivated Persons : The data placed in the hands of an ‘inexpert may lead to fallacious results. The figures may be stated without their context and thus fallacious conclusions may be reached. The argument that a country vaccinated died of small-pox, therefore vaccination is useless” is statistically defective, since we are not told what percentage of the persons who were not vaccinated died. The argument may be applied to a phenomenon other than the one to which they really relate. Also figures relating to part of a  group are taken as relating to the whole or figures favourable to an argument are stated omitting the other side. The data may be inaccurately compiled, deliberately manipulated and unscientificqlly interpretéd and made to produce a false statistical argument. The number of road accidents in Delhi in 2004 may be more than in 2002. However, there may be no need for any alarm. The increase may be due to population increase and wider use of automobiles. Thus statistics are capable of being conveniently interpreted and generally there is distrust of statistics in the mind of the public.

Sometimes certain basic results are attributed to statistics, as making forecasts for sales on the
basis of past statistics. The decision regarding future sales is not statistical as it cannot be entirely based on data. It may be true on the average but not always. There are many allied factors influencing the forecast. Circumstances can also change. Thus statistics is only a helping tool it is a means to achieve some end.

5. Statistics  cannot Prove Anything : Statistics only describe a phenomenon quantitatively, classify i into parts, summarise a fact I-elating to each part and prepare the ground for logical inference. But the inference must be drawn to the appropriate surroundings which may be personal, political or social otherwise is would not be valid. Statistics cannot give a result that can be an end in itself as is possible in many physical sciences. A drug to cure a disease is discovered by a biochemist.
A statistician is in a position to tell whether the tests carried out by him as to the efficiency of a drug are adequate or not. It is obvious that statistics plays an•auxiliary role and not a basic one.

Scope

In the begining the area of statistics was limited and it was mainly concerned with the administration of government that is why it was  termed as the science of kings. But in modern time, its area has become large and day-by-day it is gaining popularity. Normally, the facts which are represented in numerals come under statistics. Nowadays it is being used almost in all the areas of studies. According to Croxton and Cowden, “today there is hardly a phase of endeavour which does not find statistical devices at least occasionally useful”. That is why it is not unfair to say that “Science without statistics bears no fruit and statistics without science have no root”. According to Carrol D. Wright (1887), united states commissioner of the Bureau of Labour, has explained the importance of statistics in saying so.

“To a very striking degree our culture has become a statistical culture. Even a person who never
have heard of index numbers is affected by those index numbers which describe the cost of living. It is impossible to understand psychology, sociology, economics or a physical science without some general idea of the meaning of a average, of variation, of concomitance of sampling, of how to interpret charts and tables”.

Q. 2. What are the basic sources of business data? Also explain the various methods of collecting data.

Ans. Sources of Data : Data sources may be external and/or internal. External data sources may be divided into : (i) Primary sources in which original research and material gathered are summarised. These may be taken from field studies whether on a sample or census basis or from case studies. (ii) Secondary sources which use the data collected through primary sources for certain specific purposes or for general presentation in summary form and (iii) Tertiary sources which further distil data from secondary sources. Quite often, however, no distinction is made between secondary and tertiary sources. A large part of the data presented in published sources is initially collected by means of statistical surveys. Statistical material obtained from secondary sources is not always as reliable as that from the primary sources. “It is never safe to take published statistics at their face value, without knowing their means and limitations and it is always necessary to criticise arguments that can be based on them.”

Methods of Collecting Data

The collection of data for various types of investigations may be done with the help of the

following two methods : (i) Census method and (ii) Sample method.   Every survey involves the collection of the desired information from a population set or the universe, i.e. the totality of the persons, firms or items under study. This population set depends on the purpose of the survey. If an agency is interested in studying the total population in India, it would need to canvass the schedules to all the households in the rural and urban areas in India. If, on the other hand, it is interested, let us say, in learning about the economic conditions of agricultural labourers/cultivators in a particular district, it will canvass the schedules only with the agricultural labourers or cultivator-households in the district concerned.

A survey which includes every element of the population of universe under study is called a census survey.

A population can be finite or infinite. For example, the population consisting of all bolts produced in a factory on a given day is finite, whereas the population consisting of all Possible outcomes (heads, tails) in successive tosses of a coin is infinite.

The census method is generally used in the following cases : (i) when the field of investigation is
limited. (ii) when more accuracy is desired and (iii) when money spent and time taken for collection of data have no consideration.

The census method is considered to be more reliable because the data are obtained after studying each and every individual of the population.

This method has the following limitations : (i) This method is practically not possible in certain cases, e.g., to purchase one kilogram of grapes because it is not feasible to taste the complete lot to test the quality of grapes. (ii) Due to maximum consumption of time, sometimes the data collected becomes obsolete and loses its consistency, (iii) Follow-up is very difficult because it is difficult to carry out the investigation again in case of any doubt in the result obtained.

It is often impossible or impractical to observe the entire group, especially when it is large. Instead of examining the entire group, called the population or universe, one examine a small part of the group called a sample. If a sample is representative of a population, important conclusions about the population can often be inferred from analysis of the sample. The phase of statistics dealing with conditions under which such inference is valid is called inductive statistics or statistical inference, Because such inference cannot be absolutely certain, the language of probability is often used in stating conclusions. We use the sample method in the following cases : (i) field of investigation is infinite (ii) field of investigation is unlimited (iii) field of investigation leads to fatal ends (iv) field of investigation leads to devastation and (v) economy is considered necessary in investigation.

1. Lottery Method : Under this method, all items of the universe are numbered or named on separate slips or cards of paper. These slips are then folded and mixed up in a Container or drum. A blind fold selection is then made of the number of slips required to constitute the desired sample size. For the reliability of this method it is necessary that (i) all slips should be homogeneous in shape, size, colour etc., (ii) the slips should be throughly shuffled before selection of units for sample and (iii) the work of drawing slips should be done by unbiased person. This method can be explained by an example. Suppose, there are 3,000 students in a college and a random sample of 1 students is to be drawn, then 3,000 slips numbering from 1 to 3,000 will be prepared and a sample of 100 slips will be drawn one by one. It may be mentioned that the slips must be shuffled after each draw.

2. By Rotating the Drum : This method is an improvement over the lottery method. In this method separate slips are not prepared for all numbers but round or square Wooden, plastic or iron Pieces of equal size are used on which digits like O, 1; 2, 3, 4, 5, 6, 7, 8 and 9 are Written. These pieces are put in the drum and the drum is rotated by mechanical device and the number of sample is formed on written on the Piece which is drawn one by One. The digit first forms the unit-digit of the random number. The digit of the next piece forms the tenth place in the number, This process continues like that and digits for hundreds, thousands and so On, places are drawn out. This method is very Popular in drawing the number of lottery ticket for prizes.

3. Random Numbers : If the population size is very large, then difficulties arise in lottery  method and the method rotate in the drum. Further more these methods become time consuming with chances of errors. In such cases random number tables are used as alternatives.

Q. 3. Write a short note on frequency distribution.

Ans. Frequency Distribution : Arrayed series, however, does not reduce the volume of the data. In order to avoid repetition of the variables of the same magnitude we combine them together and arrange them into two columns under the headings : (1) variables and (2) its frequencies. Frequency of the value of the variable means the Snumber of times that value of the variable is repeated, i.e., the number of times of the occurrence of the value of the variable in any one series. Series represented by a discrete variable are called discrete series. Following are the examples of discrete and continuous frequency distributions :

1.  Discrete Frequency Distribution

 No. of Children No. of Families 0 10 1 40 2 80 3 100 4 250 5 150 6 50 Total  680

2.    Continuous frequency distribution

 Weight (Ibs) No. of Persons 100-110 10 110-120 15 120-130 40 130-140 45 140-150 20 150-160 04 Total 134

Although the theoretical distinction between continuous and discrete variation is clear and precise, but in practical work it is only an approximation. The reason is that even the most precise instruments of measurement can be used only to a finite number of places. Thus, every theoretically continuous series can never be expected to flow continuously with one measurement’ touching another without any break in actual observations.

Formation of Discrete Frequency Distribution : The process of preparing this type of distribution is very simple. We have just to count the number of times a particular value is repeated which is called the frequency of that to facilitate counting prepare a column of “tallies,”.

(i) We write the marks (called the variable) in the first column in serial order, i.e., from 0 to 10 or from 10 to 0 according to convenience. (ii) Against for each value of the variable in the second column we draw vertical bars whenever that particular value of the variable is to be recorded. These are drawn to facilitate counting. After a particular value has occurred four times, for the fifth we put a cross tally mark (l) on the first four tally marks to give us a block of 5. This technique of putting cross tally marks at every 5th repetition (giving groups of 5 each) facilitates the counting of the number of occurrences of the value at the end. see table below.

8. A table should always make a specific mention of the source of the data, wherever possible, as well as a note about various data gaps. This will clearly help the user of the table in understanding the limitations of the data and consequently those of the resulting Conclusions.

9. Unit of measurement should be clearly indicated.

Construction of a Table : Every table should comprise the parts enumerated as follows :

Title : Every statistical table should have a title at the top. The title should be self-explanatory
and should indicate the nature of the data being presented. It should be clear and short.

Head note : A table should have a head note below the title. A head note indicates the
designation of units in which table values are given.

Stub : The rows in a table are designated as stub items. The stub items should be complete and clear.

Caption : The columns in a table are designated as column heads. All the column heads taken
together from the caption. The column heads should also be well-defined.

Field (or Body) : The field of table shows all the numerical information to be presented in a
table. The relevant information is put against the stubs and caption in a table. This information is
presented in the form of the field (or body) of the table.

Footnote : If at the time of giving details in the table, a complete explanation of an item has not
been given, then the same is given by way ofa footnote. The footnote is given below the main table.

References : If the data have been collected from some secondary source, then’the source of the data should be disclosed. It is done in the form of giving references at the end of the table. The references should be complete in all respects.

Q. 5. Write a detail note on various bar diagrams, with suitable examples.

Ans. Bar Diagrams or One-Dimensional Diagrams : Bar diagrams are the most common type of diagrams used in practice. A bar is a thick line whose width is shown merely for attention. They are called one-dimensional because it is only the length of the bar that matters and not the width. When the number of items is large, lines may be drawn instead of bars to economies space.

While constructing bar diagrams the following points should be kept in mind .

a)    The width of the bars should be uniform throughout the diagram.

b)   The gap between one bar and another should be uniform throughout.

c)    Bars may be either horizontal or vertical. The vertical bars should be preferred because they give a better look and also facilitate comparison.

Example : The sales of Chitra Prakashan (India) Pvt. Ltd. from 2010 to 2012 are given below :

Q. 6. Give the published sources of secondary data.

Ans. Published Sources : Some of the published sources providing secondary data are :

1. Government Publications : A number of government, semi-government and Private organisations collect data related to business, trade, prices, consumption, production, industries income, health, population etc: These publications are very powerful source of secondary Central Statistical Organisation (C.S.O.), National Sample Survey Organisation (NIS.S.O.), office of the Registrar General and Census Commissioner of India, Directorate of Economics and Statistics and Labour Bureau-Ministry of labour are a few government publications.

2. International Publications : Various governments in the world and international agencies regularly publish reports on data collected by them on various aspects. For example, U.N.O.’s statistical year book, demography year book etc. can be named in this category.

3. Semi-official Publications : Local bodies like District Boards, Municipal Corporations publish periodicals providing information about vital factors like health, births, deaths etc.

4. Reports of Committees and Commissions : At times state and central governments appoint committees and commissions with a specific reference to study a phenomenon. The reports of these committees and commissions provide important secondary data. For example, Kothari commission report on education reforms, report of National Agricultural Commission, Wanchoo commission report on taxation and pay commission reports etc.

5. Private Publications : The following private publications may also be enlisted as the source
of secondary data :

(a) Journals and Newspapers : Eastern economists, monthly statistics of trade, financial express, economic times are some of the journals and newspapers which regularly collect and publish data on various aspects of business, economics, commerce and trade.

(b) Research Publications : A number of research organisations, university departments and
institutes like Indian Statistical Institute (I.S.I.) Calcutta and Delhi, I.C.A.R., N.C.E.R.T., I.C.M.R., etc. also contribute significantly to the availability of secondary data.

(c) Publications of Business and Financial Institutions : A number of business and financial institutions like chamber of commerce and Trade Association, Institute of Chartere Accountants, Sugar Mill Association, Stock Exchanges, Trade Unions and cooperative societies, etc. also contribute significantly for the availability of secondary data in the related areas.

(d) Articles : Market reviews and reports also provide data for analysis.

Limitations of Secondary Data

1.    These may not be free from personal bias and prejudices.

2.    These may not be adequate.

3.    These may not be relevant in the present contest.

4.    These may not have the needed accuracy or reliability.

Q. 10. What is histogram? Explain with example of equal class-interval and unequal class-interval.

Ans.

Histogram (Equal class-interval)

Histogram is one of the most popular and widely used method of presenting a frequency distribution. A histogram is a set of rectangles whose areas are in proportion to class frequencies. Thus it is not only a graphical record of absolute class frequencies but also provides a comparison of class frequencies.

A histogram may be best constructed on a graph paper, which is ruled with equally spaced
horizontal and vertical lines. For example, let us consider the histogram for the following frequency

Here inclusive classes are given and as a first step, these should be converted into classes with
true or actual class limits as given in the second column of the table 1. These true class limits are then plotted along with the horizontal axis (x-axis) and class frequencies on the vertical axis (y-axis) with the help of a suitable scale of measurement. Generally, a vacant class is also allowed at either end of the horizontal scale as shown in fig. (a). This improves the readability of the graph and is also useful in the construction of a frequency polygon which will be discussed in the next section.

In order to give symmetry and balance to histogram (or any graphic presentation), one needs to be careful in the selection of unit distances to represent class limit on x-axis and the frequencies on y-axis. For representing these distances, the scales of measurement on two axes are so selected that the height of the histogram (or any other graphic presentation) is approximately 75 per cent of its width. This ratio may, however, vary from 65-85 per cent for conveniently representing various frequency distributions with a balanced figure.

Having marked off the two scales, a rectangle over each class is constructed in such a way that its area is proportional to the corresponding class frequency. This can be done very easily when we are given classes with equal class-intervals. In such a case equal width of the class is treated as one unit and rectangles over classes are so formed that their heights are proportional to class A histogram representing the frequency distribution of scores in table 1 is shown in figure this, the height of the rectangle formed over class 19.5-29.5 is 4 units along the vertical sale (representing frequency) and as such its area becomes 4 x 1=4 square units, which is equal to the frequency of the class. Similarly, heights of other rectangles formed over consecutive classes are taken as 6, 8, 12, 9, 7 and 4 respectively so that their areas too are equal to corresponding class frequencies.

In table 2, the class-interval of second and fourth class is twice that of the rest of the classes. Thus, the frequencies in second and fourth classes are not comparable with other classes. To establish this comparability, the frequencies in the larger classes should be halved or divided by two. Thus, before forming histogram for frequency distribution with unequal class-intervals, all larger classes should be expressed as multiples of smaller classes; and then divide the corresponding class frequencies by these multiples. This division, then, gives the height of rectangles (as given in the last column of table 2) to be formed over given classes. Now, if the class-interval 10 of the class 19.5-29.5 is taken as one unit then class-interval 20 of the class 29.5 – 49.5 will be equal to 2 units. Thus, a rectangle of height 7 formed over 29.5 – 49.5 will represent an area 7 x 2 14 which is in accordance with the principle Of histogram, equal to class frequency. Similarly, the height of the rectangle to be formed over class 59.5-79.5 will be 8 so that its area 8 x 2 —16 will represent the class frequency. However, heights of other rectangles formed over classes of unit lengths will remain equal to corresponding class frequencies. The histogram obtained for the frequency distribution of scores in table 2 is given in figure (b).

We have seen that histogram is a graphical representation of a frequency distribution. It is
supposed to represent all the characteristics of a good table. Histogram too should be given a clear brief and self-explanatory title. Index showing the scales of measurements on both axes should be given in the upper right corner of the figure and units of measurements should be mentioned along the axes so as to make the graph easily readable.

Q. 11. What is false base line? Explain its utility in construction of graphs. (2018)

Ans. If the fluctuations in a dependent variable is less and the difference between its minimum
value and zero is more, then for effective presentation of a graph, false base line is used. This can be done if, instead of showing the entire scale from zero to the highest value involved, only as much is shown as is necessary for the purpose and that portion which lies between zero and the lowest value of the variable is left out. In other words, the portion lying between zero and minimum necessary value is omitted by tampering with the base line. This commission in the vertical scale starts with zero but after putting a false base line at a distance of about 1 or 2 cms, the scale gets a fresh start with a value equal (or nearly equal) to the smallest value of the variable. It is shown in figure :

It may be mentioned that the use of false base line may also be used for X-axis.

The device of false base line is useful in proper depiction of the fluctuations of the variable
values, when they are smaller as compared with the size fo the figures. In graph of such data without false base line, the zero of the vertical scale will lie far below the actual range of variations and whole of the curve will go at the top vertical scale will lie far below the actual range of variations and whole of the curve will go at the graph. In the absence of a significant variation in the values, it may appear like a straight line. As such, in addition to the poor visual communication, it would make waste to a large part of the graph sheet. But the use of the false-base line changes the scenario altogether.

However, its use needs caution, otherwise the Y-scale may sometimes result into a wrong visual impressions. The reasons being : (a) the lowest value plotted at the false-base goes very close to zero’ (b) the fluctuations receive two different interpretations : one with respect of the original base line’ i.e., X-axis and the other with respect to the false base line. So, this device should be used only when it becomes necessary. The use of false base line can be understood by the example given :

Example : Plot the following data on a graph paper :

 Year 2000 2001 2002 2003 2004 2005 2006 2007 No of medical tourists : 123 139 134 140 157 148 192 198

Sol. In this question, values are big and fluctuations are comparatively small. hence, it will be
appropriate to use false base line for effective presentation Of data and fluctuations therein. The minimum and maximum values are 123 and 198 respectively, Thus, scale on Y-axis is taken from 120 to 200 and 1 cru 10 (00) medical tourist is taken.

of Graphic Presentation of Data : The two main types of graphical

presentation of research results are line graphs and bar charts. Graphs can be small. so multiple plots

can be presented on a single page or screen. Line graphs can show more detail than bar charts-

line Graphs : Line graphs are useful to display more than one relationship in the same picture,

for to fertilizer of three different varities.

Bar Charts : Bar charts display simple results clearly, They are not generally useful for large

amounts of structured information. It is frequently useful to -cluster” bars aggording to

the categories they represent, to highlight certain comparisons, The method of grouping should be

determined by the objective of the chart.

It is easier for readers to make comparisons between adjacent bars than between distant bars

and the chart should be laid out accordingly,

Graphic displays rules are as follows :

1.     Show the data,

2.     Avoid distorting the data.

3.    Induce the viewer to think about the substance of the graphic rather than the methodology, graphic design, or something else,

4.     Make large amounts of data coherent.