Economics 6 Marks Question

Firstly, we will convert the given data into less than frequency distribution.

Marks	c.f. (Less than)
Less than 5	3
Less than 10	13
Less than 15	33
Less than 20	63
Less than 25	83
Less than 30	92
Less than 35	97
Less than 40	100

The temperature is positive, as well as, negative. So, this data can be presented with the help of sub-divided bar diagram.
The diagrammatic representation of the given data is shown below:

First, we prepare a percentage table.

Percentage Table
	2011-12		2012-13
Subject	Number of Students (in '000)	Percent	Number of Students (in '000)	Percent
Statistics	25	25	30	30
Economics	40	40	42	42
History	35	35	28	28
Total	100	100	100	100

Now, we draw bars of equal length (100%) corresponding to each year. Then, each bar is divided according to percentage of different years.
A percentage sub-divided bar diagram of given data is shown below:

S. No.	Component	Description
1.	Title	Title is a brief and clear explanation of the contains of the table.
2.	Table Number	A number is assigned to a table for easy identification when man tables are included.
3.	Date	Date of the creation of the table should be indicated.
4.	Row Designations	Each row of the table is given a brief name, usually provided in the first column. Such a name is known as a "stub", and the column is known as the "stub column".
5.	Column Headings	Each column is given a heading to explain the nature of the figures included in each column. Such names are known as "captions" or "headings".
6.	Body of the table	Data is entered into the main body and should be created for easy identification of each data items. Numeric values are often ordered in either ascending or descending order.
7.	Unit of Measurement	The unit of measurement of the values in the table body should be indicated.
8.	Sources	The tables should provide the primary and secondary sources for the data below the body of the table.
9.	Footnotes and References	Addition details for clarifying the contents of the table.

As in the question, sugar production is given for two years. For presenting the data in tabular form, data should be categorised in different parts namely-month, year. Total production, off-take for internal consumption and off-take for exports.
The given data is tabulated below:
Suger Production in India

Month, Year	Total Production (in tonnes)	Off-take for Internal Consumption (in tonnes)	Off-take Exports (in tonnes)
December, 2000	3,78,000	1,54,000	-
December, 2001	3,87,000	2,83,00	41,000

The above table shows data related to three variables, therefore it is represented through a multiple bar diagram.
The bar diagram showing index number of agricultural production is given below:

Graph showing exports and imports from year 2005 to 2011 is given below:

1. Tabular presentation of data presents data in rows and columns, whereas diagrammatic presentation of data translates the abstract ideas shown in numbers into more concrete form, easy to comprehend.
2. Tabulation organises data for further statistical treatment and decision making but the diagrams may be less accurate but are comparatively more effective than tables in presenting the data.
3. Tabular presentation can be done by using one-way, two-way on three-way classification depending upon the number of characteristics involved, whereas there are various kinds of diagrams which are commonly used like geometric diagram, frequency diagram, arithmetic line graph etc.

This data can be tabulated as below:
Productions of Foodgrains in India

(2015-16)

Foodgrains	Total Production (in lakh tonne)	Production (in %)
Rice	1000	40
Wheat	900	36
Other crops	600	24
Total	2500	100

Note: Other foodgrains include other cereal crops.

The following are the advantages of graphical presentation:

1. Simple Form: It presents the complex data in a simple or understandable form.
2. Forecasting: It is used for forecasting, interpolation and extrapolation. This helps to assess the future changes in the value of the variable.
3. Study of Variations: With the help of graphs, we can study the variations in the values of variables and can take corrective actions.
4. Attractive: Graphical presentation helps to present the data in an attractive manner which makes it interesting and impressive.
5. Essay Comparison: Graphical presentation of data facilitates easy comparison between the values of the data.
6. Universal Utility: Graphical presentation is popularly used in journal, news papers, board meeting, etc to give the required information to the general users.
7. Helpful in Computing Statistical Averages: Statistical averages such as median, quartile, deciles, etc can be easily computed with the help of graphical presentation.

Graphical presentation of data suffers from the following limitations:

1. Actual/ Precise Values are not Disclosed Graphical presentation merely shows the tendency and fluctuations. Actual and precise values are not disclosed through a graphical presentation, so it does not show precise values.
2. Lead to Wrong Conclusions It may sometimes suggest wrong conclusions and give misleading information.
3. Limited Information Graphical presentation can be used to depict only one or two characteristics. Because of this, only limited information can be presented through this presentation.

A frequency polygon can also be converted back into a histogram by drawing vertical lines from the bounds of the classes shown on the horizontal axis, and then connecting them with horizontal lines at the hieghts of the polygon at each mid-point. Frequency Polygon can be drawn in two ways:Method:

1. Draw a suitable Histogram as explain in the previous section following all the basic principles.
2. Get the mid points of the upper horizontal side of each rectangle.
3. Join these mid points of the adjacent rectangles of the histogram by straight lines.
4. Ends of the frequency polygon are to be extended to mid point of classes at both sides.
5. Labelling should be properly done and scale of measurement should be clearly shown.

An example is shown below.

The following are the advantages of graphical presentation:

1. Simple Form: It presents the complex data in a simple or understandable form.
2. Forecasting: It is used for forecasting, interpolation and extrapolation. This helps to assess the future changes in the value of the variable.
3. Study of Variations: With the help of graphs, we can study the variations in the values of variables and can take corrective actions.
4. Attractive: Graphical presentation helps to present the data in an attractive manner which makes it interesting and impressive.
5. Essay Comparison: Graphical presentation of data facilitates easy comparison between the values of the data.
6. Universal Utility: Graphical presentation is popularly used in journal, news papers, board meeting, etc to give the required information to the general users.
7. Helpful in Computing Statistical Averages: Statistical averages such as median, quartile, deciles, etc can be easily computed with the help of graphical presentation.

Graphical presentation of data suffers from the following limitations:

1. Actual/ Precise Values are not Disclosed Graphical presentation merely shows the tendency and fluctuations. Actual and precise values are not disclosed through a graphical presentation, so it does not show precise values.
2. Lead to Wrong Conclusions It may sometimes suggest wrong conclusions and give misleading information.
3. Limited Information Graphical presentation can be used to depict only one or two characteristics. Because of this, only limited information can be presented through this presentation.

Time Series Graph

Firstly, we will convert the given data into more than frequency distribution.

Marks	c.f. (more than)
More than 0	50
More than 10	45
More than 20	35
More than 30	20
More than 40	8

Different types of graphs are explained below:

1. Line Frequency Graph: Line diagrams consist in drawing vertical lines, length of each line being equal to frequency. The values of variate x are presented on a suitable scale along y-axis. Line diagrams facilitate comparison but they are not attractive to see.
2. Histograms: These graphs are used to graph grouped data. It is one of the most popular and commonly used devices · for charting continuous frequency distribution. It consists of erecting a series of adjacent vertical rectangles on the section of X-axis with bases of equal width of the corresponding class intervals and the heights are so taken that the area of the rectangle are equal to the frequency of the corresponding classes.
3. Frequency Polygons: A frequency polygon is formed by marking the mid-point at the top of horizontal bars and then joining these dots by a series of straight lines. The frequency polygons are formed as a closed figure with the horizontal axis, therefore a series of straight lines are drawn from the mid-point of the top base of the first and the last rectangles to the midpoint falling on the horizontal axis of the next outlaying interval with zero frequency.
4. Frequency Curve: It is described as a smooth frequency polygon. A frequency curve is described in terms of its (i) symmetry (skewness) and (ii) degree of peakedness (kurtosis).Two frequency distributions can also be compared by superimposing two or more frequency curves provided the width of their class intervals and the total number of frequencies are equal for the given distributions. Even if the distributions to be compared differ in terms of total frequencies, they still can be compared by drawing per cent frequency curves where the vertical axis measures the per cent class frequencies and not the absolute frequencies.
5. Time Series Graph: When information is arranged over a period of čime, it is called time series graph. In it, time (hour, day/date, week, month, year, etc.) is plotted along x-axis and the value of the variable (time series data) along y-axis. A line graph by joining these plotted points, thus, obtained is called arithmetic line graph (time series graph).

Export and Import Graph

1. Pie diagram.
2. Deviation Bar diagram.
3. Deviation Bar diagram.
4. Simple bar diagram.
5. Percentage bar diagram.
6. Multiple Bar diagram.

Marks	Mid-value	f
0-10	5	5
10-20	15	12
20-30	25	15
30-40	35	22
40-50	45	14
50-60	55	4

S. No.	Diagrammatic Presentation of Data	Tabular Presentation of Data.
1.	Diagrams and Graphs are meant for a lay man.	Tables are meant for statisticians for the purpose of further analysis.
2.	Diagrams give only an approximate idea.	Tables contain precise figures. Exact values can be read from tables.
3.	Diagrams can be more easily compared, and can be interpreted by a layman.	Comparison and interpretations of tables can only be done by statisticians and it is a difficult task.
4.	Diagrams and graphs cannot present much information.	Tables can present more information.
5.	Diagrams are more attractive and have a visual appeal.	Tables are dry for a layman (may be attractive to a statistician).

Histogram

Marks (Midpoints)	40-50	50-60	60-70	70-80	80-90
No. of Students (f)	5	9	12	8	2

Items	Angles
Agriculture	40 × 3.6° = 144°
Industry	21 × 3.6° = 75.6 = 76°
Transport	19 × 3.6°= 68.4 = 68°
Administration	13 × 3.6° = 46.8 = 47°
Banking	7 × 3.6° = 25.2 = 25°

Simple and complex tables: The distinction between simple and complex table is based on the number of characteristics studied.
In a simple table only one character is shown. Hence this type of table is also known as one-way table. On the other hand in a complex table two or more characteristics are shown. When two characteristics are shown such a table is known as two-way table or double tabulation.
Example of one way table: Number of employees in state bank according to age group.

Age (in years)	No. of employees
Below 25	3
25-35	2
35-45	2
Above 45	3

Example of two-way table: Number of employees of state bank in different age groups according to sex.

Age (in years)	Employees		Total
	Males	Females
Below 25	3	2	5
25-35	4	5	9
35-45	5	6	11
Above 45	2	3	5
Total	14	16	30

When three or more characteristics are represented in the same table is called three-way tabulation. As the number of characteristics increases, the tabulation becomes so complicated and confusing.

To construct a frequency polygon without histogram the following values will be plotted.

Mid Value (X)	Number of Workers (f)
5	10
15	18
25	35
35	30
45	20
55	12
65	8
75	3

Subject	Marks	%	Angle °
English	60	15.38	55.36°
History	75	19.23	69.22°
Economics	80	20.51	73.83°
Maths	95	24.35	87.66°
Geography	80	20.51	73.83°

Simple Bar Diagram

Expenditure Item	Amount (₹)	%	Angle (°)
Salary and Wages	45,000	45	162°
Rent	15,000	15	54°
Interest Patment	8,000	8	29°
Repair	20,000	20	72°
Capital Formation	12,000	12	43°
Total	1,00,000	100	360°

1. Sub-divided Bar Diagram

2. Multiple Bar Diagram

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The preparation of a good table is an art. The purpose of tabulation must always be kept in mind before the preparation of a statistical table. A good statistical table must contain at least the following components.
In general, a statistical table consists of the following eight parts. They are as follows:

1. Table Number: Each table must be given a number. Table number helps in distinguishing one table from other tables. Usually tables are numbered according to the order of their appearance in a chapter. For example, the first table in the first chapter of a book should be given number 1.1 and second table of the same chapter be given 1.2 Table number should be given at its top or towards the left of the table.
2. Title of the Table: Every table should have a suitable title. It should be short & clear. Title should be such that one can know the nature of the data contained in the table as well as where and when such data were collected. It is either placed just below the table number or at its right
3. Caption: Caption refers to the headings of the columns. It consists of one or more column heads. A caption should be brief, concise and self-explanatory, Column heading is written in the middle of a column in small letters.
4. Stub: Stub refers to the headings of rows.
5. Body: This is the most important part of a table. It contains a number of cells. Cells are formed due to the intersection of rows and column. Data are entered in these cells.
6. Head Note: The head-note (or prefactory note) contains the unit of measurement of data. It is usually placed just below the title or at the right hand top corner of the table.
7. Foot Note: A foot note is given at the bottom of a table. It helps in clarifying the point which is not clear in the table. A foot note may be keyed to the title or to any column or to any row heading. It is identified by symbols such as *,+,@,£ etc.
8. Source Note: The source note shows the source of the data presented in the table. Reliability and accuracy of data can be tested to some extent from the source note. It shows the name of the author, title, volume, page, publisher's name, year and place of publication of the book or journal from which data are complied.

'THE TITLE' Prefatory Notes:
	Box Head
Row Captions	Calumn Captions
Stub Entries	The Body

Foot Notes
Source Note Solution

Marks	c.f. (less than)
Less than 5	7
Less than 10	17
Less than 15	37
Less than 20	50
Less than 25	62
Less than 30	72
Less than 35	87
Less than 40	95

Marks	c.f. (more than)
More than 0	95
More than 5	88
More than 10	78
More than 15	58
More than 20	45
More than 25	33
More than 30	23
More than 35	8

1. Normal Curve: In this curve, highest frequency is at the centre and both tails on the left and right hand side are in identical fashion. It is a unimodal curve in which mean, median and mode are equal. It is also known as bell shaped or symmetrical curve. It is shown below:

Normal Curve Showing the Percent of Cases Lying Within 1, 2, and 3 Standard Deviations from the Mean.

2. Positively Skewed Curve: It is asymmetrical curve which has a tail on the left hand side of the graph and frequencies are more for the higher values of the data. The left tail is longer, the mass of the distribution is concentrated on the right of the figure. It has relatively few low values. The distribution is said to be left-skewed. It is shown below:

3. Negatively Skewed Curve: It is asymmetrical curve which has a tail on the right hand side of the graph and frequencies are more for the lower values of the data. These histograms have the curve on the left side of the distribution. If the right tail is longer, the mass of the distribution is concentrated on the left. It has relatively few low values. It is shown below:

4. Symmetrical Distribution Curve: It is like normal curve but normal curve is unimodal. We can say it to be twins of normal curves. In this curve, highest frequencies are at two places one at a lower value and other at a higher extreme value and hence, it is also called bimodal curve of symmetrical distribution. It is shown below:

5. J Shaped Curve: When class frequencies running maximum towards higher values and not at the centre, it gives a J shaped frequency curve. It is called so because it appears like English Letter J. It is shown below:

6. U Shaped Curve: In this case, maximum frequency is at the ends of the data and minimum are the centre. It is shown below:

7. Reverse J Shaped Curve: When class frequencies are running up to a maximum at one end and not at the centre and it is lower end not higher one, it gives inverse J shaped curve. It is shown below:

8. Mixed Curve: Sometimes, it is difficult to find a trend in the frequencies. The frequencies rise and fall at different intervals. It is called Mixed Curve. There cannot be one particular shape of mixed curve. It is also called non monotonic curve because it does not show any particular pattern. One example is shown below:

A good table is one which is able to convey the required information effectively. The guidelines for preparing a good table are stated below:

1. Simple and Compact: The table should be simple and compact, so that it should not create confusion in the mind of the user.
2. Focus Attention on Main Comparisons: The data in the table should be arranged so that it focuses attention on the main comparisons and clearly exhibits the relationship between various related items. For this, different fonts of lettering (italic, bold, capital letters, etc) may be used.
3. Complete and Self-Explanatory: A table should be complete and self-explanatory. It should contain all the essential parts of a table. Also, in the preparation of table, use of abbreviations should be avoided. Only common abbreviations should be used.
4. Attractive: A table should be designed so that it is neither too long or narrow, nor too broad or short. If the data is very large, it should not be crowded in a single table, rather a number of different tables of reasonable size and shape should be prepared. All this helps in attractive presentation of data.
5. Accurate and Free from Errors: The data contained in the table should be accurate and free from errors. For this, the entries in the table should be checked and re-checked.
6. Classification According to a Specific Attribute: The classification of data in a table should be according to a specific attribute.

Merits:

1. Attractive and Impressive: Diagrams are attractive and impressive.
2. Simple and easily understandable: Diagrams are easy and simple to understand. Knowledge of mathematics is not required to understand diagrams.
3. Useful in Comparison: Diagrams prove very useful in comparing data from one year to another or otherwise.
4. Helps in forecasting: It helps us to predict future values on the basis of past statistics.
5. Save time effort and energy: By simplifying data, diagrams save time, energy and effort.
6. Diagrams are useful in all fields: From sports to education to medical and engineering, in all fields we make use of diagrams. They are specifically useful for policy formulation and decision making.

Limitations: Diagrams are a very useful tool in presentation of data but they cannot be a substitute for classification or tabulation. It is not free from limitations.

1. Diagrams do not present the small differences properly.
2. These can easily be misused.
3. Only artist can draw multi-dimensional diagrams.
4. In statistical analysis, diagrams are of no use.
5. Diagrams are just supplement to tabulation.
6. Only a limited set of data can be presented in the form of diagram.
7. Diagrammatic presentation of data is a to more time consuming process.
8. Diagrams present preliminary a conclusions.

After the collection of data, the next step is to present them in some suitable form-statistical table is one of them. Tabulation enables the numerical facts to be presented in such a way that their analysis, interpretation and subsequent computation become easier. Decision makers neither have the opportunity nor have enough time to go through bulky data. They want the information in a precise form so that conclusions can be want the information in a precise form so that conclusions can be drawn from them without much wastage of time and energy. Tabulation is thought to be useful tool in this respect. The condensed facts presented in table can be easily visualized and the needed information can be easily sorted out. The comparability of the data increases significantly when they are placed side by side in a table. This also helps the establishment of relationship between different phenomena. Tabulation paves the way for further condensation of the data by presenting them in suitable forms for mathematical treatment. Statistics is the study of large numbers. The study of a large number of cases is difficult unless some process of condensing the information is available The principal objectives of tabulation are stated below:

1. To make complex data simple: When data are arranged systematically in a table, such data become more meaningful and can be easily understood.
2. To facilitate comparison: When different data sets are presented in tables it becomes possible to compare them.
3. To economize space: A statistical table furnishes maximum information relating to the study in minimum space. Statistical tables conserve space and reduce explanatory and descriptive statements to a minimum.
4. To make data fit for analysis and interpretation: Tabulation serves as a link between the collection of data on the one hand and analysis of such data on the other. In other words, after tabulating the data, it becomes possible to find out their averages, dispersion and correlation. Such statistical measures are necessary for their interpretation.
5. To provide reference: A statistical table can be used as a source of reference for other studies of similar nature.
6. Memorizing effect: The visualization of relations and process of comparison are greatly facilitated by tables. Tabulated data can be more easily remembered than data that are not tabulated.
7. Facilitates Detection of errors: A tabular arrangement facilitates the summation of items and the detection of errors and omissions and Statistical tables provide a basis for computations.

No, not all tables fulfill these objectives. Only tables drawn keeping essentials of a good table fulfill these objectives.

A frequency distribution gives the number of observations that lie in any class interval whereas the cumulative frequency distribution gives the number of frequencies that lie below any mark or above any given mark. When derived from a frequency distribution, the cumulative frequency distribution of one kind gives the number of observations less than the lower boundaries of the successive class and the cumulative frequency distribution of the second kind gives the number of observations that exceed the lower boundaries of the class which are respectively known as the less than and greater than the cumulative frequency distribution. If we draw frequency polygon to the above two distribution we get cumulative frequency polygon (less than & greater than). If we draw a frequency curve to the above two distribution in the same graph, we get cumulative frequency curve or Ogive.Steps Involved:

1. Find the cumulative frequencies of the given frequencies by "less than method' or 'more than method' as you need.
2. Less than type cumulative frequencies will give less than type ogive and more type cumulative frequencies will give less than type ogive.
3. Variable under study is taken on X-axis.
4. Cumulative Frequencies are taken on Y-axis.
5. Both the axis should be clearly labeled and scale of measurement should be clearly shown.
6. Various points are plotted on graph.
7. By joining these points we get ogive or cumulative frequency curve.

Items	% of expenditure	Angular component
A	30	30 × 3.6° = 108°
B	20	20 × 3.6° = 72°
C	15	15 × 3.6° = 54°
D	35	35 × 3.6° = 126°
Total	100	360°

For less-than and more-than ogives we will have to prepare less-than and more-than frequency distributions.

Less-than Distribution		More-than Distribution
Weekly Wages (in ₹)	Number of Workers	Weekly Wages (in ₹)	Number of Workers
Less than 20	10	More than 10	100
Less than 40	30	More than 20	90
Less than 60	70	More than 40	70
Less than 80	90	More than 20	30
Less than 100	100	More than 10	10

The 'less-than' and ‘more-than' ogives of the given data are shown below:

Merits:

1. Attractive and Impressive: Graphs are attractive and impressive.
2. Simple and easily understandable: Graphs are easy and simple to understand. Knowledge of mathematics is not required to understand graphs.
3. Useful in Comparison: Graphs prove very useful in comparing data from one year to another or otherwise.
4. Helps to understand trend: Graphs help us to understand trend in a variable.
5. Helps to measure statistical averages: Graphs are used to measure some statistical tools like median, mode, quartiles and correlation etc. (Helps to understand shape of the distribution: We can use graphical presentation to understand if a curve is normal or skewed; if it is upward sloping or downward sloping etc.
6. Helps in forecasting: It helps us to predict future values on the basis of past statistics.
7. Graphs are useful in all fields: From sports to education to medical and engineering, in all fields we make use of graphs. They are specifically useful for policy formulation and decision making.

Disadvantages of Graphic Presentation:

1. Time Consuming: Graph making is a time consuming task.
2. Layman Can't Understand: A layman cannot understand and interpret the data represented graphically.
3. Not suitable for all types of data: Graphs are not suitable for all types of data.

A good diagrammatic presentation should have the following features:

1. The presentation should be attractive.
2. It should communicate the required information effectively.
3. The presentation should be accurate.
4. The diagrams drawn to present the data should be proportionate in height and width.
5. As far as possible, the diagrammatic presentation should be self-explanatory. Words and calculation should be avoided in a diagrammatic presentation.
6. The presentation should be simple and easy to understand.
7. The size of the diagram should be proportionate to the size of the paper.
8. In diagrammatic presentation, vertical diagrams should be preferred over horizontal presentation.
9. A diagrammatic presentation should be accompanied with suitable headings.
10. The scale of the presentation should be carefully selected and should be indicated along with the presentation.
11. Different colours and signs should be used for presenting data on different variables. In this presentation, diagrams should be drawn either from left to right or from bottom to top.
12. The data on the basis of which the diagrams are drawn, should be clearly mentioned.

Different steps in construction of a pie diagram are given below:

1. Convert all the values as a percentage of total value.
2. Convert the various observations in percent) in the data set into corresponding degrees in the circle by multiplying each by 3.6 (360%100).
3. If you wish to convert the values directly into degrees, you can use a formula.
4. Draw a circle of appropriate size with a compass. Size of circle depends on space available and number of sub items in pie diagram. If two or more pie chart are beings drawn which are to be compared then radii of all these must be equal.
5. Draw points on the circle according to the size of each portion of the data with the help of a protractor and join each of these points to the center of the circle. It is a common practice to keep the largest components at 12 O'clock position in the circle.
6. Different components should be distinguished from each other by using either different shades or colours.
7. A proper index explaining shades or colours used for different items should be drawn.

Simple Bar Diagram

A good table should essentially have the following parts:

1. Table number.
2. Title.
3. Caption or Column Head.
4. Stub or Row Head.
5. Body of the table.
6. Source note.
7. Foot note.

• Table Number is essential for the purpose of identification. If in a chapter more than one table is presented then it is essential to number them like 2.1, 2.2 ......, etc. It is given at the top of the table.
• Title tells us about the content of the table. It has to be short, clear and carefully worded. It is placed below the table number.
• Caption At the top of each of the column in a table a column designation is provided to explain the columns. This is known as "Caption” or “Column Head”.
• Stub Each row of the table has to be given a heading. The designation of the heading to the rows is called “Stub”. The left most column of the table is known as Stub with Stub Head and Stub Entries.

1. On the basis of construction:

Simple table: It is a table which reflects only one variable at a time. It is very simple to draw. It is also called one-way table. Its example is given below:
Number of Employees in an organization according to age Group

Age (in Year)	No. of Employees
Below 25	50
25-35	67
35-45	43
45-55	15
5 and above	5
Total	180

1. Complex tables: It is a table which represents two or more variables in one table. It may be two way or three way or more than type of variables.

1. Two-way table: It represents two variables. An example of two way table is given below:

Tables showing grades of boys and girls of class

	Grade
	A	B	C	Total
Boys	13	25	11	49
Girls	7	20	6	33
Total	20	45	17	82

2. Three-Way Table gives information regarding three mutually dependent and inter-related questions. For example, from one-way table, we get information about age, and from two-way iable, we get information about the number of male and female available in various grades. A three way table is showing.

• Population in various division.
• Their sex-wise distribution
• Their position of literacy.

Division	Three-Way Table
	Population (Millions)
	Male			Female			Tatal
	Litrarate	Illiterate	Total	Literate	Illiterate	Total	Literate	Illiterate	Total
Delhi
Mumbai
Chennai
Kolkata

3. Higher Order Tables: Manifold (or Higher Order) Table: Such tables provide information about a large number of interrelated characteristics in the data set.

State	Neonatal Mortality			Post-neonatak Mortality			Child Mortality (12-47 months)
	Male	Female	F/ M ratio	Male	Female	F/ M ratio	Male	Female	F/ M ratio
Northern region
Delhi	36.2	30.3	0.83	24.1	34.1	1.41	13.6	21.2	1.56
Haryana	47.1	37.6	0.80	28.8	45.9	1.59	18.4	34.2	2.34
Hinmachal Pradesh	41.6	34.4	0.83	25.6	28.5	1.11	17.6	25.3	1.44
Punjab	32.9	27.0	0.82	22.8	22.1	0.97	12.7	23.0	1.81
North-central region
Bihar	64.0	50.0	0.78	37.3	42.4	1.13	34.5	53.5	1.55
Madhya Pradesh	63.1	49.5	0.78	36.5	43.4	1.19	46.7	56.8	1.22
Rajansthan	43.3	42.0	0.97	31.3	37.5	1.20	26.5	42.2	1.59
Uttar Pradesh	71.1	68.3	0.96	41.5	51.6	1.24	38.5	65.5	1.70
Eastern region
Assam	63.0	47.9	0.76	37.9	36.4	0.96	52.9	59.6	1.13

The following general guidelines are taken into consideration while preparing diagrams:

1. Title: Each diagram should have a suitable title. It may be given either at the top of the diagram or below it. The title must convey the main theme which the diagram intends to portray.
2. Size: The size and portion of each component of a diagram should be such that all the relevant characteristics of- the data are properly displayed and can be easily understood.
3. Proportion of length and breadth: An appropriate proportion between the length and breadth of the diagram should be maintained. As such there are no fixed rules about the ratio of length to width.
4. Proper scale: There are again no fixed rules for selection of scale. The diagram should neither be too small nor too large. The scale for the diagram should be decided after taking into consideration the magnitude of data and the size of the paper on which it is to be drawn. The scale showing the values as far as possible should be in even numbers or in multiples of 5, 10, 20, and so on. The scale should specify the size of the unit and the nature of data it represents, for example, 'millions of tonnes', in ₹ thousand, and the like. The scale adopted should be indicated on both vertical and horizontal axes if different scales are used. Otherwise, it can be indicated at some suitable place on the graph paper.
5. Footnotes and source note: To clarify or elucidate any points which need further explanation but cannot be shown in the graph, footnotes are given at the bottom of the diagrams.
6. Index: A brief index explaining the different types of lines, shades, designs, or colours used in the construction of the diagram should be given to understand its contents.
7. Simplicity: Diagrams should be prepared in such a way that they can be understood easily. To keep it simple, too much information should not be loaded in a single diagram as it may create confusion. Thus if the data are large, then it is advisable to prepare more than one diagram, each depicting some identified characteristic of the same data.

Firstly, we will convert the given data into less than and more than frequency distribution.

Marks Scored	Number of Students	c.f. (less than)	c.f. (more than)
10-20	5	5	50
20-30	10	15	45
30-40	30	45	35
40-50	5	50	5

Items of expenditure	% age of total expenditure	Angular component
Food	60	60 × 3.6º = 160º
Education	15	15 × 3.6º = 54º
Housing	10	10 × 3.6º = 36º
Clothing	10	10 × 3.6º = 36º
Miscellaneous	5	5 × 3.6º = 18º
Total	100	360º

Items	Expenditure	Angular component
Labour	25	25 × 3.6° = 90°
Bricks	15	15 × 3.6° = 54°
Cement	20	20 × 3.6° = 72°
Steel	15	15 × 3.6° = 54°
Timber	10	10 × 3.6° = 36°
Supervision	15	15 × 3.6° = 54°
Total	100	360°

Histogram and Frequency Polygon

Time Series Graph

Wages (in ₹)	No. of Worlers (f)
325-350	20
350-375	45
375-400	60
400-425	35
425-450	10