Research Methodology
Unit IV
Editing:- The raw data is likely to contain a no. of errors during the process of recording the information in surveys. By means of editing one tries to eliminate the errors or remove the points of confusion, if any.
For proper analysis & interpretation, it is necessary that the collected data are present, readable & accurate in the desired form i.e., data collected has no missing values, all entries are readable or all information is accurate. This introduces errors in collected information, which are to rectified before further analysis.
Editing comprises inspecting, correcting & mo0difying the raw data to ensure that information available is correctly, adequately & relevantly.

Stages of Editing:- The editing may be done in two stages:
Field Editing:- The field editing is done immediately after collection of data because the interviewer then have a fresh memory about the lapses & wrong statements of answers. The preliminary editing should be done by a field supervisor.
Office Editing:- The office editing is done after the field editing. This implies a complete & thorough scrutiny of questionnaire. There should be expert editors in the office to evaluate & examine the completed returns of the respondents. The incorrect answers may also be verified by observation. When the answers are given in an ambiguous manner, serious efforts are made to rectify & complete them by consulting another questionnaire.

Factors to be considered while Editing:-
Fictitious Interviews:- the interviewer may complete himself the questionnaire without contacting the respondent. Sometimes poor quality of interviewing & poor quality responses are the main cause of errors in raw data.
Responses not legible:- if the interviewer or the respondent’s handwriting is bad then the recorded information may not be legible in some cases. The larger the no. of open-ended questions, the more prominent will be the problem of stops or illegible responses.
“Don’t Know” & “No Answer”:- a ‘no answer’ occurs when the respondent leaves the question blank in a mail questionnaire. The editors should not always follow a foolish practice of throwing out all ‘don’t know’ & ‘no answer’ questionnaires. These situations are likely to occur in all type of studies. These must be anticipated & adjusted by the researcher.
Inadequate answers:- The answers supplied by the respondent are either incomplete or ambiguous.
Irrelevant answers:- Here the answers provided by the respondents is out of context. This may be due to the inability of respondent to understand the question properly or he may not be competent to provide required information properly.

Guidelines for Editing:-
There should be written editing instructions explaining how to handle each question of the questionnaire.
The corrections should be made in a different color to distinguish the original & edited data.
The information from interviews should be edited promptly.
The editor should have interview with each interviewer to ascertain his recording style, handwriting etc.
Editor should make the changes in original data either by crossing it or transferring it instead of erasing it.
If some observation is missing, the editor can enter estimated data or the respondent can be contacted on the telephone or the investigator can be requested to collect the necessary information again.

Coding:- Coding is the procedure of classifying the answers to a question into meaningful categories. The symbols used to indicate these categories are called codes. Coding refers to the process of assigning numerals or other symbols to answers so that responses can be put into a limited no. of categories or classes. Such classes should be appropriate to the research problem under consideration. Coding is necessary to carry out the subsequent operations of tabulating & analyzing data. If coding is not done, it will not be possible to reduce a large no. of heterogeneous responses into0 meaningful categories with the result that the analysis of data would be weak & ineffective, and without proper focus.
Coding involves two steps:
The first step is to specify the different categories or classes into which the responses are to classify.
The second step is to allocate individual answers to different categories.

Procedure of Coding:- Before coding it is necessary to prepare a coding frame. Coding frame is set of clearly printed instructions on both the groupings of the answers & on the codes which are to be assigned to each group. The instructions can be framed by taking a sub-sample from the collected data & producing a detailed list of all the answers obtained for various kinds of enquiries. For each kind of enquiry there may be considerable overlapping both in terms of word & sense. Answers having common words & sense are placed together.
In certain situations a combination of the two approaches can be followed. The codes framed should be properly examined with respect to the objectives of the survey, suitability for further analysis & to ensure that they are not ambiguous.

Guidelines for determining the code frame:
When Numerical data is coded:
Know what type of analysis will be performed. Build the categories & their intervals around the study’s objectives & hypothesis.
Set intervals so that the numbers most frequently cited are near the intervals mid point.
Establish categories so that the intervals are mutually exclusive.
Establish categories that coincide with categories in other studies with which comparisons are to be made.
Use multiple categories when doubt exists about how the data will be analyzed.

When Qualitative data is to be coded:
The final decision about categories should be made after a representative no. of responses have been reviewed.
Use a category which facilitates comparison with other data. Use categories which are precise & mutually exclusive.
Include all possible answers.

Tabulation:- Tabulation may be defined as the logical & systematic organization of statistical data in rows & columns. It is designed to simplify presentation & facilitate analysis.
Tabulation is one of the most important & ingenious devices of present5ing the data in a condensed & readily comprehensible form. It attempts to furnish the maximum information in the minimum possible space, without sacrificing the quality & usefulness of the data.
Essentials of Tabulation:-
Suit the purpose:- A table should be in keeping with the object of statistical enquiry.
Scientifically Prepared:- The table should be prepared in a systematic & logically organized manner, simple & compact so that it is readily comprehensible. It should be free from all sorts of over-lapping & ambiguities.
Clarity:- A table should be easily understandable, complete & self-explanatory.
Manageable Size:- A table should be so designed that it is neither very long & narrow nor very short & broad. If needed, it should be adjusted to the space provided for the purpose.
Columns & Rows should be numbered:- When there are a no. of rows & columns in a table, they must be numbered for reference.
Average & Totals:- The averages & percentages should, as far as possible, be given to the right or at the bottom of the columns containing original figures.
Proper Lettering:- It is not advisable to use too many styles of letters in a table. Large capital letters & bold face type may be used for headings, stubs, captions & small letters may be used for prefatory notes, footnotes & source notes. Lettering also helps in adjusting the size of the table.

Structure of a Table or Main Parts of a Table:- The various parts of the table are:

Table Number:- Each table should be numbered. The no. may be given either in the centre at the top above the title or inside of the title at the top or in the bottom of the table on the left-hand side.
Title of the Table:- Every table must be given suitable title. The title is the description of the contents of the table. A complete title has to answer the question what, where & when in that sequence.
Caption:- Caption refers to the column headings. It explains what the column represents. It may consist of one or more column headings. Under a column heading there may be sub-heads. The caption should be clearly defined & placed at the middle of the column.
Stubs:- These refers to the headings of the horizontal rows & they are written on the left hand side of the rows. Whether there is need for stubs, and if yes, how many, would depend on the nature of the data.
Footnotes:- Anything in a table, which the reader may find difficult to understand from the title, caption & stubs should be explained in the footnotes. If footnotes are needed they are placed directly below the body of the table.
Body:- The body of the table contains the statistical data, which have to be presented. This is the most vital part of a table & the data contained in the body are arranged according to the captions & stubs.
Head note:- Statistical table contain a headnote, which refers to the data contained in the major part of the table, and it is placed below the title of the table. Generally written as headnote like ‘in lakhs’, or ‘in tonnes’ etc.

Following is the Structure or Format of a table indicating the above parts:

|Table No. |
| |Title |Head Note |
|Stub Heading |Caption |
| |Column Heading |Column Heading |Column Heading |Total |
|Sub Entries | B | O D | Y | |
|Total | | | | |
|Footnotes |
|Source |

Types of Tables:- Tables may broadly be classified into two categories:

Simple & Complex Tables:- The distinction between simple & complex table is based upon the no. of characteristics studied. In a simple table only one characteristic is shown. Hence, this type of table is known as one-way table. In a complex table, on the other hand, two or more characteristics are shown. Such tables are more popular in practice because they enable full information to be incorporated & facilitate a proper consideration of all related facts. The following examples will illustrate the distinction between simple & complex tables.
Simple or one-way table:- In this type of table only one characteristic is shown. This is the simple type of table. The following is the illustration of such a table:
Example: No. of employees in State Bank according to the age group as:
|Age (in years) |No. of Employees |
|Below 25 | …………………. |
|25-35 |…………………. |
|35-45 |…………………. |
|45-55 |…………………. |
|Above 55 |…………………. |
| | |
| |Total ………………… |

Two-way Table:- Such a table shows two characteristics & is formed when either the stub or the caption is divided into two coordinate parts. The following example illustrates the nature of such a table:

Example: No. of employees of State Bank in different age-groups according to sex as:

|Age (in years) |Employees |Total |
| |Males |Females | |
|Below 25 | _________ | _________ | _____ |
|25-35 |_________ |_________ |_____ |
|35-45 |_________ |_________ |_____ |
|45-55 |_________ |_________ |_____ |
|Above 55 |_________ |_________ |_____ |
|Total | __________ | _________ | _____ |

Higher Order Table:- When three or more characteristics are represented in the same table, such a table is called higher order table. The need for such a table arises when we are interested in presenting a no. of characteristics simultaneously.

General & Special Purpose Tables:- General purpose tables also known as reference tables or repository tables provide information for general use or reference. They usually contained information & are not constructed for specific discussion. Such tables tell facts which are not for particular discussion. When such tables are used by a researcher, they are usually placed in the appendix of the reports for easy reference.

Example: Point out the mistakes in the following table drawn to show the distribution of population, according to sex, age & literacy.
|Gender |0 to 25 |25 to 50 |50 to 75 |75 to 100 |
|Males | | | | |
|Females | | | | |

Solution: All the characteristics are not revealed in the above table; the characteristic of literacy has been completely ignored. Even otherwise, the tables need to be rearranged as follows:
|Table: Showing the Distribution of Population according to Age, Sex & Literacy. |
|Age Groups |Literates |Illiterates |Total |
| |M |F |
|1998 |195 |80 |
|1999 |200 |87 |
|2000 |165 |45 |
|2001 |140 |32 |

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Sub-divided Bar diagram:- In a sub-divided bar diagram, the bar is sub-divided into various parts in proportion to the values given in the data & the whole bar represent the total. Such diagrams are also called component bar diagrams.
Example: Represent the following data by a sub-divided bar diagram:
| |Monthly Expenditure |
| |(in Rs.) |
|Expenditure | |
|Items | |
| |Family A |Family B |
|Food |75 |95 |
|Clothing |20 |25 |
|Education |15 |10 |
|Housing Rent |40 |65 |
|Miscellaneous |25 |35 |

Two-dimensional diagrams:- In one dimensional diagram, only length is taken into account. But in two-dimensional diagrams the areas represent the data & so the length & breadth have both to be taken into account. Such diagrams are also called area diagrams or surface diagrams. The important types of area diagrams are:
Rectangles:- Rectangles are used to represent the relative magnitude of two or more values. The area of the rectangles is kept in proportion to the values. Rectangles are placed side by side for comparison. When two sets of figures are to be represented by rectangles, either of the two methods may be adopted.
Squares:- The method of drawing the square diagram is very simple. One has to take the square root of the values of various items that are to be shown in the diagrams & then select a suitable scale to draw the squares.
Pie Diagram or Circular Diagram:- In such diagrams, both the total & component parts or sectors can be shown. The area of a circle is proportional to the square of its radius. While making comparisons, pie diagrams should be used on a percentage basis & not on an absolute basis.
In constructing a pie diagram, the first step is to prepare the data so that various component values can be transposed into corresponding degrees on the circle.
The second step is to draw a circle of appropriate size with a compass. The size of the radius depends upon the available space & other factors of presentation.
The third step is to measure points on the circle & representing the size of each sector with the help of a protractor.
Example: Draw a pie diagram for the following data of production of sugar in quintals of various countries.
|Country |Production of Sugar |
| |(in quintals) |
|Cuba |62 |
|Australia |47 |
|India |35 |
|Japan |16 |
|Egypt |6 |

Solution: The values are expressed in terms of degree as follows:
| |Production of Sugar |
| | |
|Country | |
| |In Quintals |In Degrees |
|Cuba |62 |134 |
|Australia |47 |102 |
|India |35 |76 |
|Japan |16 |35 |
|Egypt |6 |13 |
|Total |166 |360 |

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Graphs:- A graph is a visual form of presentation of statistical data. A graph is more attractive than a table of figure. Even a common man can understand the message of data from graph. Comparisons can be made between two or more phenomena very easily with the help of graph.

Uses of the graphs:-
It simplifies the complexities of large numbers or that of large mass of data.
Graphs can easily depict the trend of the subject under study.
As compared to the preparation of suitable diagrams to represent the statistical data. They may be easily depicted on a graph paper.
Classification & tabulation processes are both difficult & time consuming. As compared to them, the graphical method is both easy & representative.
Contrary to other methods of representation of statistical data, the graphical method is commonly followed. It can be prepared & used even by common men with little education.

Types of Graphs:- Some important types of graphs which are more popular & they are:

Histogram:- A histogram is a bar chart or graph showing the frequency of occurrence of each value of the variable being analyzed. In histogram, data are plotted as a series of rectangles. Class intervals are shown on the ‘X-axis” & the frequencies on the “Y-axis’.
Example the data given below by histograms:
Income (in Rs.): 0-50 50-100 100-150 150-200 200-250 250-300
Frequency : 10 40 80 90 30 20

Frequency Polygon:- If we mark the midpoints of the top horizontal sides of the rectangles in a histogram & join them by a straight line, the figure so formed is called frequency polygon.
Example: Illustrate the following by frequency polygon:
|Scores |Frequency |
|90-99 |02 |
|80-89 |12 |
|70-79 |22 |
|60-69 |20 |
|50-59 |14 |
|40-49 |3 |
|30-39 |1 |
|20-29 |1 |

Frequency Curve:- If the middle point of the upper boundaries of the rectangles of a histogram is corrected by a smooth free hand curve, then that diagram is called frequency curve. The curve should begin & end at the base line.
Example: Draw a frequency curve from the following frequency distribution:
|Scores |Frequency |
|140-144 |2 |
|135-139 |2 |
|130-134 |2 |
|125-129 |4 |
|120-124 |5 |
|115-119 |9 |
|110-114 |6 |
|105-109 |4 |
|100-104 |3 |
|95-99 |2 |
|90-94 |1 |

Charts:- A chart is a visual representation of data, in which the data are represented by symbols such as bars in a bar chart or lines in a line chart. A chart can represent tabular numerical data, functions or some kinds of qualitative structures.

Significance of Chart:-
Charts are often used to ease understanding of large quantities of data & the relationships between parts of the data.
Charts can usually be read more quickly than the raw data that they are produced from.
They are used in a wide variety of fields & can be created by hand or by computer using a charting application. Certain types of charts are more useful for presenting a given data set than others.

Types of Charts:-
Bar charts:- Bar charts consist of bars running either vertically or horizontally with an individual bar for each observation. The individual bars have separate have separate observations. Bar charts have become more popular than bar diagrams or line diagrams. The vertical charts are used for classified data & chronological quantity. In the case of qualitative or geographic data, horizontal bar charts are used to depict them more precisely.
Pictograph:- The pictograph uses tiny pictures or symbols to represent the idea or subject. This device is used to give a more vivid picture of the report. It is appropriate for bar-type charts. It is not intended for detailed study & precise measurement, but to give one short glimpse of the findings.
Pie Charts:-
Pyramid:- Pyramid consists of many levels & presents one or two variables. Horizontal bars in a pyramid indicate the strength of the variables.

Analysis of Variance:- The analysis of variance was developed by R.A. Fisher. Analysis of Variance is useful in the fields of economics, biology, education, psychology, sociology & business/industry and in researches of several other disciplines. This technique is used when multiple sample cases are involved. For example, the significance of the difference between the means of two samples can be judged through either z-test or the t-test, but the difficulty arises when we happen to examine the significance of the difference amongst more than two sample means at the same time.
The ANOVA technique is important in the context of all those situations where we want to compare more than two populations such as in comparing the yield of crop from several varieties of seeds, the gasoline mileage of four automobiles, the smoking habits of five groups of university students & so on.
Through ANOVA technique one can, in general, investigate any no. of factors, which are hypothesized or said to influence the dependent variable. One may as well investigate the differences amongst various categories within each of these factors, which may have a large no. of possible values.

Characteristics of ANOVA:-
It makes statistical analysis of variances of two, or more series, or samples.
It determines whether the difference in the mean values of the different samples is due to chance or due to any significant cause, and thereby it reveals the true characteristics of the given series.
It gives the desired result by finding the appropriate variance ratio through the f-test technique.

Assumptions of ANOVA:-
It is assumed that the universe from which the different samples are drawn for study is normally distributed.
It is assumed that the samples under study have been drawn at random, and that they are homogeneous & independent of each other.
It is assumed that there is no significant difference amongst the variances of the different universes from which the samples have been drawn.
It starts with the null hypothesis that V1= V2=V3=…….Vn (where V1,V2,V3,……Vn are variance)

Basic Principle of ANOVA:- The basic principle of ANOVA is test for differences among the means of populations by examining the amount of variation within each of these samples, relative to the amount of variation between the samples. In terms of variation within the given population, it is assumed that the values of (Xij) differ from the mean of this population only because of random effects.
Thus while using ANOVA, we assume that each of the samples are drawn from a normal population & that each of these populations has the same variance. We also assume that all factors other than the one or more being tested are effectively controlled.
In short, we have to make two estimates of population variance viz., one based on between samples variance & the other based on within samples variance. Then the said two estimates of population variance are compares with f-test, wherein we work out.

F = Estimate of population variance based samples variance Estimate of population variance based on within samples variance

This value of F is to be compared to the F-limit for given degrees of freedom. If the F value we work out is equal or exceeds the F-limit value, we may say that there are significant differences between the sample means.

Advantages of ANOVA:-
ANOVA allows us to compare multiple means all at once.
ANOVA keeps the experiment-wise error rate to the set level.
Avoid inflation in error rate due to multiple comparisons.
Can detect an effect of the treatment even when no. 2 groups are significantly different.
Compared with using multiple t-tests, one-way & two-way ANOVA require fewer measurements to discover significant effects.
ANOVA is far more general & far more flexible than randomization tests.

Types of Variance:- The different types of variance which we are to analyze under the technique of F-test may be broadly classified into two types, viz.,
Variance due to One Variable:- The variance in the value of a variable, say the yield of the crop that is studied with reference to the effect of another variable only, say seed on fertilizer or soil is called variance due to one variable. Such variances are taken into account in one way classification for which we are to conduct the experiment through a no. of sample studies.
Thus, if the effects of three types of irrigation facility on the yield of a crop are to be studied, we may take 3 samples of 5 fields each, and analyze the variance to come to a conclusion as to its significance. The data for analysis for such variance are presented. Sample of production in two different plots are:
A: 12 13 18 17 15
B: 14 17 12 11 16

Variance due to two variable:- The variance in the value of a variable, say sale that is studied with reference to the combined effect of two other variables, say efforts of salesmen, and season is called variance due to two way variables. Such variance is taken into account in two way classification for which also, we are to conduct the experiments through a no. of sample studies.
Thus, if the combined effect of the salesmen & the seasons on the sales is to be studied, the collected samples of sales are arranged in the binary form as under:

One-way ANOVA Technique:- Under the one-way ANOVA, we consider only one factor & then observe that the reason for said factor to be important is that several possible types of samples can occur within that factor. We then determine if there are differences within that factor. The technique involves the following steps:
1) Obtain the mean of each sample i.e., obtain:

2) Work out the mean of the sample means as follows:

3) Take the deviations of the sample means from the means of the sample means & calculate the square of such deviations which may be multiplied by the no. of items in the corresponding sample, and then obtain their total. This is known as the sum of squares for variance between the samples (or SS between).
Symbolically, this can be written:

4) Divide the result of the 3rd step by the degrees of freedom between the samples to obtain variance or mean square (MS) between samples. Symbolically, this can be written as:

5) Obtain the deviations of the values of the sample items for all the samples from corresponding means of the samples & calculate the square of such deviations & then obtain their total. This total is known as the sum of squares for variance within samples (or SS within). Symbolically this can be written as:

6) Divide the result of 5th step by the degrees of freedom within samples to obtain the variance or mean square (MS) within samples. Symbolically this can be written as:

7) To check, the sum of squares of deviations for total variance can also be worked out by adding the squares of deviations when the deviations from the individual items in all the samples have been taken from the mean of the sample means. Symbolically this can be written as:

This total should be equal to the total of the result of the (iii) & (v) steps explained above, i.e.,
SS for total variance = SS between + SS within.
The degrees of freedom for total variance will be equal to the no. of items in all samples minus one i.e., (n-1). The degree of freedom for between & within must add up to the degree of freedom for total variance i.e.
(n-1) = (k-1) + (n-k)
This fact explains the additive property of the ANOVA technique.

8) Finally, F-ratio may be worked out as under:

F-ratio = MS between MS within
This ratio is used to judge whether the difference among several sample means is significant or is just a matter of sampling fluctuations. For this purpose, we look into the table, giving the values of F for given degrees of freedom at different levels of significance. If the worked out value of F is less than the table value of F, the difference is taken as insignificant. In case the calculated value of F happens to be either equal or more than its table value, the difference is considered as significant which means the samples could not have come from the same universe & accordingly the conclusion may be drawn.
The higher the calculated value of F is above the table value, the more definite & sure one can be about his conclusions.

Measures of Central Tendency:- The statistical measures which tell us the location or position of central value or central point to describe the central tendency of the entire mass of data is known as measure of central tendency or measure of central value or measure of location or average of first order.

Characteristics of Measures of Central Tendency:-
It should be rigidly defined.
It should be easy to calculate & simple to follow.
It should be based on all observations in the series.
It should not be affected much by a few extreme values.
It should be capable of further algebraic treatment.
It should be capable of being used in further statistical computation or processing.

Kinds of Averages:-
Arithmetic Mean:- Arithmetic Mean of a group of observations is the quotient obtained by dividing the sum of all the observations by their no. Arithmetic Mean is denoted by X or A.M. Thus,

X = sum of all the observations Number of Observations
Advantages of Arithmetic Mean:-
It is easy to calculate & simple to understand.
It is based on all the observations.
It is capable of further algebraic treatments.
It is not necessary to arrange the observations is ascending or descending order.

Geometric Mean:- The geometric mean of ‘n’ numbers is defined as the “nth root of the product of ‘n’ numbers”. It is found out by multiplying all the values of a series & extracting nth root of the product.

Symbolically, G.M. = n (X1) x (X2) x (X3)……..x (Xn)
X1, X2, X3……. Refer to the various values in the series. N = no. of items.

Merits of Geometric Mean:-
It is based on all observations.
It is rigidly defined.
It is capable of further algebraic treatment.
It is less affected by the extreme values.
It is useful in studying economic & social data.

Harmonic Mean:- The Harmonic is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the individual observations.

Thus, H.M. = N . 1 + 1 + 1 + ……………….+ 1 X1 X2 X3 Xn
Merits of Harmonic Mean:-
It is rigidly defined.
It is based on all observations.
It is capable of further algebraic treatment.
It is less affected by the extreme values.
It gives greater importance to small items.

Median:- If a group of N observations is arranged in ascending or descending order of magnitude, then the middle value is called median of these observations & is denoted by M or Me. That is, M= N+1th observation. 2
Advantages of Median:-
The median, unlike mean, is unaffected by the extreme values of the variable. It is capable of further algebraic treatment. It is used in calculating mean deviation.
It can be determined graphically.
It is easy to calculate & simple to understand.
Median can be calculated in case of open-end class.
Median is defined rigidly.

Mode:- The word Mode is made from the French language ‘La Mode’ which means Fashion of System. The value of the variable for which the frequency the maximum is called mode or modal value & is denoted by Z or Mo.

Advantages of Mode:-
It is easy to calculate & simple to understand.
It is not affected by the extreme values as in the average.
It is usually an actual value as it occurs most frequently in the series.
It is simple & precise.
The value of Mode can be determined by the graphic method.

Relation between Mean, Mode & Median:
Empirically the relation is as Mode= 3Median – 2Mean

Measure of Dispersion:- A measure of dispersion is designed to state the extent to which individual observations or items vary from their average.

Objectives of Measuring Dispersion:-
To judge the reliability of Measures of Central Tendency.
To compare two or more series with regard to their variability.
To control the variability itself.
To facilitate the use of other statistical measure.

Properties of a Good Measure of Variation:-
It should be easy to compute.
It should be simple to understand.
It should be rigidly defined.
It should be based on each & every item of the distribution.
It should be capable of further algebraic treatment.

Range:- Range is the difference between the highest & the lowest value in a series. This is the simplest absolute measure of dispersion.
Symbolically, R = L – S
Where, R = Range, L = Maximum largest value & S = Minimum Smallest Value.

Merits of Range:-
Range is the simplest measure of dispersion.
It is simple to understand & easy to calculate.
It is rigidly defined.
It gives the limit within which all of the items occur.

Mean Deviation:- Mean Deviation of a series is the arithmetic average of the deviations of various items from the median or mean of that series.

Coefficient of Mean Deviation:-
Coefficient of M.D. from Mean = Mean Deviation (M.D.) Arithmetic Mean
Coefficient of M.D. from median = Mean Deviation (M.D.) Median
Coefficient of M.D. from mode = Mean Deviation (M.D.) Mode

By: Ajay Nath Dubey