Class 11 Economics Chapter 4 — Presentation of Data (ASSEB)
Welcome to HSLC Guru! In this lesson, we explore Chapter 4 — Presentation of Data from the ASSEB Class 11 Statistics for Economics syllabus. After the data are collected and organised, the next important step is to present them in a clear, attractive and meaningful way so that comparisons, patterns and conclusions become easy to understand. This chapter explains the three major modes of presentation — textual, tabular and diagrammatic/graphical — along with the construction of bar diagrams, pie diagrams, histograms, frequency polygons, frequency curves, ogives and arithmetic line graphs.
Summary of the Chapter
Meaning and Need of Presentation: Once raw data are classified, they must be presented in an organised manner so that users can read, analyse and interpret them with ease. Presentation makes complex figures simple, helps in comparison of two or more variables, saves time and space, and supports decision-making in economics, business and government. Broadly, data are presented in three forms — textual (descriptive) presentation, tabular presentation, and diagrammatic or graphical presentation. The choice depends on the nature of data, the audience and the purpose of the study.
Textual and Tabular Presentation: In textual presentation, the data are described as part of running text, which is suitable when the figures are very few. Tabular presentation arranges data in rows and columns. A statistical table has standard parts — table number, title, head-note, captions (column headings), stubs (row headings), body, source note and footnote. A good table should be simple, attractive, properly numbered, and self-explanatory. Tables may be classified as simple, double, treble or manifold; and as general-purpose (reference) or special-purpose (text/summary) tables.
Diagrammatic Presentation: Diagrams give a quick visual impression and have great memorising effect. The main diagrams are bar diagrams and pie diagrams. Bar diagrams use rectangular bars of equal width, drawn vertically or horizontally; their length is proportional to the value of the variable. They are of three main types — simple bar diagram (one variable), multiple bar diagram (two or more related variables compared side by side) and sub-divided / component bar diagram (each bar is divided into parts to show the components of a total). A pie diagram is a circle whose total area (360°) is divided into sectors in proportion to the components; each component’s angle = (component value ÷ total) × 360°.
Graphical Presentation of Frequency Distributions: Graphs are used mainly for continuous frequency distributions and time series. The important graphs are — histogram (adjacent rectangles drawn on class intervals with heights equal to frequencies/frequency densities; used for continuous data); frequency polygon (line graph obtained by joining the mid-points of the tops of the rectangles of a histogram, or by plotting class mid-values against frequencies); frequency curve (a smoothed frequency polygon); and ogive or cumulative frequency curve (less than ogive and more than ogive, used to find the median graphically). The arithmetic line graph (time-series graph) shows the value of a variable plotted against time on the X-axis and is widely used to study trends in production, prices, population, exports, etc.
Textbook Question Answers
A. Very Short Answer Type Questions (1 Mark)
Q1. What is meant by presentation of data?
Answer: Presentation of data means arranging the classified statistical data in the form of text, tables or diagrams/graphs so that they become easy to understand, compare and analyse.
Q2. Name the three main modes of presentation of data.
Answer: (i) Textual presentation, (ii) Tabular presentation, and (iii) Diagrammatic or graphical presentation.
Q3. What is a statistical table?
Answer: A statistical table is a systematic arrangement of numerical data in rows and columns, with appropriate headings, so that the relationship between figures can be seen clearly.
Q4. Define caption and stub.
Answer: Caption is the heading given to the columns of a table, while stub is the heading given to the rows on the left-hand side of the table.
Q5. What is a simple bar diagram?
Answer: A simple bar diagram consists of bars of equal width but varying lengths, drawn to represent the values of a single variable such as production, population or income.
Q6. What is a pie diagram?
Answer: A pie diagram is a circular diagram in which the total of 360° is divided into sectors in proportion to the values of the various components of an aggregate.
Q7. What is a histogram?
Answer: A histogram is a two-dimensional diagram consisting of adjacent rectangles drawn on class intervals of a continuous frequency distribution, with heights proportional to the frequencies of the classes.
Q8. What is an ogive?
Answer: An ogive is the graphical representation of a cumulative frequency distribution. It may be drawn as a “less than” ogive or a “more than” ogive.
Q9. What does an arithmetic line graph show?
Answer: An arithmetic line graph shows the changes in the value of a variable over time; time is taken on the X-axis and the value of the variable on the Y-axis.
Q10. Which graph is used to locate the median?
Answer: The ogive (cumulative frequency curve) is used to locate the median graphically.
B. Short Answer Type Questions (2–3 Marks)
Q1. State any three objectives of tabular presentation of data.
Answer: (i) To present complex data in a simple and compact form. (ii) To facilitate easy comparison between different sets of figures. (iii) To save space and time, and to help in further statistical analysis such as averages and dispersion.
Q2. Mention any four parts of a good statistical table.
Answer: The main parts of a table are: (i) Table number for identification, (ii) Title describing the contents, (iii) Captions (column headings) and Stubs (row headings), (iv) Body containing the actual figures, and (v) Source note and footnote showing the origin of the data and explanations.
Q3. Distinguish between a multiple bar diagram and a sub-divided bar diagram.
Answer: In a multiple bar diagram, two or more related variables are shown by separate bars placed side by side for each category, helping in direct comparison of magnitudes. In a sub-divided (component) bar diagram, a single bar represents the total and is divided into parts to show the components of that total. Multiple bars compare magnitudes; sub-divided bars compare composition.
Q4. Write a short note on pie diagram.
Answer: A pie diagram (circular diagram) is used to show the components of an aggregate. The whole circle (360°) represents the total. Each component is converted into degrees by the formula:
Angle of component = (Value of component ÷ Total value) × 360°
Each sector is then drawn and shaded differently. Pie diagrams are best suited to show percentage break-up of items such as government expenditure, family budget, etc.
Q5. Distinguish between a histogram and a bar diagram.
Answer: A bar diagram is one-dimensional; bars of equal width are drawn with gaps between them and are used for discrete or qualitative data. A histogram is two-dimensional; rectangles are drawn on class intervals without gaps and are used only for continuous frequency distributions, where both width (class interval) and height (frequency) carry meaning.
Q6. What is a frequency polygon? How is it different from a frequency curve?
Answer: A frequency polygon is a line graph obtained either by joining the mid-points of the tops of the rectangles of a histogram by straight lines or by plotting class mid-values against frequencies and joining them. A frequency curve is the smoothed form of a frequency polygon, drawn as a free-hand curve so that the area under it remains the same. The polygon uses straight lines, while the curve is smooth.
C. Long Answer Type Questions (5–6 Marks)
Q1. Explain the different types of presentation of data with their merits.
Answer: Statistical data can be presented in three main ways:
(i) Textual presentation: The data are described as part of running text. It is simple, requires no special skill, and is suitable when the data are very few. However, it becomes confusing when figures are large.
(ii) Tabular presentation: Data are arranged in rows and columns under suitable headings. Tables are precise, allow easy comparison, save space and form the basis of further statistical analysis.
(iii) Diagrammatic and graphical presentation: Data are shown through bars, circles, histograms, polygons or line graphs. They give a quick visual impression, are attractive, easy to remember, and useful for the general public. They are widely used in newspapers, reports and television to communicate economic information effectively.
Q2. Describe in detail the different parts of a good statistical table.
Answer: A well-constructed statistical table generally has the following parts:
(i) Table Number: Each table is given a number for identification and easy reference.
(ii) Title: A short, clear and complete title at the top tells what the table contains, the place and the period.
(iii) Head-note: Written below the title in brackets, it gives information about the unit of measurement (e.g., in lakh tonnes, in ₹ crore).
(iv) Captions: Headings of the columns, often divided into main captions and sub-captions.
(v) Stubs: Headings of the rows on the left-hand side describing the contents of each row.
(vi) Body: The most important part, containing the actual numerical data arranged according to captions and stubs.
(vii) Source Note: Given at the bottom of the table, it indicates from where the data have been collected (e.g., Economic Survey 2023–24).
(viii) Footnote: Used to explain any specific item, abbreviation or peculiarity in the table.
Q3. Explain different types of bar diagrams with examples.
Answer: Bar diagrams are one-dimensional diagrams in which the length of the bar represents the value of the variable, while the width is kept uniform. The main types are:
(i) Simple Bar Diagram: Used to represent a single variable. For example, the population of India in different census years can be shown by separate bars, each bar’s height showing the population in that year.
(ii) Multiple Bar Diagram: Used to compare two or more related variables. For instance, the production of rice and wheat in five different states can be shown by drawing two bars side by side for each state, using different shades.
(iii) Sub-divided / Component Bar Diagram: Used when the total is to be split into its components. For example, total expenditure of a family on food, clothing, education and others can be shown as one bar divided into four parts, each shaded differently.
(iv) Percentage Bar Diagram: A special type of sub-divided bar where each bar is of equal length (100%) and components are shown in percentage form, making it easier to compare composition.
Q4. Explain histogram, frequency polygon, frequency curve and ogive.
Answer: These four are the main graphs of a continuous frequency distribution:
(i) Histogram: A series of adjacent rectangles drawn on class intervals (X-axis) with heights equal to the frequencies (Y-axis). It gives a visual idea of the shape of the distribution. It is drawn only for continuous data; gaps are not allowed between the rectangles.
(ii) Frequency Polygon: Obtained by joining the mid-points of the upper sides of the rectangles of the histogram by straight lines, or directly by plotting (mid-value, frequency) points and connecting them. The polygon is closed by extending it to the X-axis at both ends.
(iii) Frequency Curve: A smooth free-hand curve drawn through the points of the frequency polygon. It removes the irregularities and gives an idea of the general shape of the distribution (symmetrical, skewed, etc.).
(iv) Ogive (Cumulative Frequency Curve): Drawn by plotting cumulative frequencies against class boundaries. The “less than ogive” rises upward to the right, while the “more than ogive” falls downward. The point of intersection of both ogives, when projected on the X-axis, gives the median of the distribution.
Q5. What is an arithmetic line graph? Mention its uses.
Answer: An arithmetic line graph, also called a time-series graph, is a graph in which time (years, months, days) is taken on the X-axis and the value of the variable on the Y-axis. The successive points are joined by straight lines to show how the variable changes over time.
Uses: (i) It shows the trend of variables such as population, production, prices, exports and imports; (ii) it helps in comparison of two or more variables over the same period when drawn on the same graph; (iii) it is used in business, economic planning and forecasting; (iv) it makes seasonal and cyclical movements easy to observe; and (v) it is simple to draw and easy to interpret even by non-experts.
Additional Multiple Choice Questions (MCQs)
Q1. Which of the following is NOT a mode of presentation of data?
(a) Textual (b) Tabular (c) Diagrammatic (d) Editorial
Answer: (d) Editorial.
Q2. The heading of a column in a table is called —
(a) Stub (b) Caption (c) Body (d) Title
Answer: (b) Caption.
Q3. The heading of a row in a table is called —
(a) Caption (b) Stub (c) Footnote (d) Source
Answer: (b) Stub.
Q4. A bar diagram is —
(a) One-dimensional (b) Two-dimensional (c) Three-dimensional (d) Pictorial
Answer: (a) One-dimensional.
Q5. A pie diagram is in the form of a —
(a) Square (b) Rectangle (c) Circle (d) Triangle
Answer: (c) Circle.
Q6. Total degrees in a pie diagram are —
(a) 180° (b) 270° (c) 360° (d) 100°
Answer: (c) 360°.
Q7. A histogram is used for —
(a) Discrete data (b) Qualitative data (c) Continuous data (d) Time series
Answer: (c) Continuous data.
Q8. The graph used to locate the median is —
(a) Histogram (b) Frequency polygon (c) Ogive (d) Bar diagram
Answer: (c) Ogive.
Q9. A smoothed frequency polygon is called —
(a) Ogive (b) Frequency curve (c) Histogram (d) Line graph
Answer: (b) Frequency curve.
Q10. An arithmetic line graph shows —
(a) Components of a total (b) Frequency distribution (c) Time series data (d) Geographic data
Answer: (c) Time series data.
Fill in the Blanks
Q1. The heading given to the rows of a table is called __________.
Answer: Stub.
Q2. __________ presentation is the simplest form of presentation of data.
Answer: Textual.
Q3. A pie diagram divides the total of __________ degrees among the components.
Answer: 360°.
Q4. A histogram is drawn for a __________ frequency distribution.
Answer: Continuous.
Q5. The point of intersection of less than and more than ogives gives the __________.
Answer: Median.
True or False
Q1. Bar diagrams are two-dimensional diagrams.
Answer: False. Bar diagrams are one-dimensional; only their length is meaningful.
Q2. A pie diagram is suitable for showing the components of a total.
Answer: True.
Q3. Histogram and bar diagram are exactly the same.
Answer: False. Histograms are used for continuous data and have no gaps; bar diagrams are used for discrete data with gaps.
Q4. A frequency polygon can be drawn without first drawing a histogram.
Answer: True.
Q5. Time is taken on the Y-axis in an arithmetic line graph.
Answer: False. Time is shown on the X-axis.
Glossary
| Term | Meaning |
|---|---|
| Presentation of Data | Arranging classified data in text, tables, diagrams or graphs for easy understanding. |
| Textual Presentation | Description of data in the form of running text or paragraphs. |
| Tabular Presentation | Systematic arrangement of data in rows and columns. |
| Caption | Heading of a column in a statistical table. |
| Stub | Heading of a row in a statistical table. |
| Body of a Table | The main part of the table containing actual numerical data. |
| Source Note | Note placed at the bottom of a table indicating the source of data. |
| Footnote | Note explaining peculiarities or items inside a table. |
| Bar Diagram | One-dimensional diagram with bars of equal width and varying length. |
| Simple Bar Diagram | Bar diagram showing a single variable. |
| Multiple Bar Diagram | Bar diagram comparing two or more related variables side by side. |
| Sub-divided Bar Diagram | Bar divided into parts to show components of a total. |
| Pie Diagram | Circular diagram showing components as sectors of 360°. |
| Histogram | Set of adjacent rectangles drawn on class intervals for continuous data. |
| Frequency Polygon | Line graph joining the mid-points of the tops of histogram rectangles. |
| Frequency Curve | Smoothed form of a frequency polygon. |
| Ogive | Cumulative frequency curve used to locate the median. |
| Arithmetic Line Graph | Time-series graph showing a variable’s value against time. |
| Median (graphical) | Value at the point of intersection of less than and more than ogives. |
| Class Interval | Range of values in a continuous frequency distribution. |