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This page provides complete NCERT exercise solutions for CBSE Class 11 Economics Chapter 4 — Presentation of Data. Review the Key Concepts first, then work through the intext questions and chapter-end exercises. For construction-based questions (tables, diagrams, ogives), follow the step-by-step method shown. Use these answers to cross-check your work and prepare effectively for exams.
Key Concepts (Quick Recap)
- Textual Presentation: data described in text; suitable for small data sets
- Tabular Presentation: data arranged in rows and columns; most common method
- Parts of a Table: Title, Stub (row headings), Caption (column headings), Body, Footnote, Source
- Types of Tables: (a) Classification by purpose — Reference table, Summary table; (b) Classification by nature — Time series, Spatial, Qualitative, Quantitative
- Diagrammatic Presentation: visual representation; types — bar diagrams, pie charts, histograms, frequency polygons, ogives
- Bar Diagram: bars of equal width, height proportional to value, bars separated; types — simple, multiple, sub-divided, percentage
- Pie Chart: circle divided into sectors; each sector angle = (Value/Total) × 360°
- **Histogram: adjacent rectangles for continuous data; width = class interval, height = frequency; no gaps between bars
- Frequency Polygon: line joining mid-points of histogram bars; can also be drawn without histogram
- Ogive (Cumulative Frequency Curve): less-than type (S-curve rising) and more-than type (S-curve falling)
- Arithmetic Line Graph (Time Series): time on X-axis, variable on Y-axis; shows trends over time
Intext Questions
Section 4.1 — Tabular Presentation
1. Data is organised systematically in rows and columns. 2. Comparison between items is easier. 3. Patterns and trends can be identified quickly. 4. Unnecessary details are eliminated. 5. It occupies less space than textual description. 6. It is more appealing and easier to read.
Section 4.2 — Diagrammatic Presentation
Chapter-End Exercise
Question 1
Define tabular presentation. What are its main parts?
Main parts of a table:
1. Title: describes the content of the table (placed at the top) 2. Stub: row headings on the left side 3. Caption: column headings at the top 4. Body: the main data arranged in cells 5. Headnote: general explanation below the title (e.g., "Figures in lakhs") 6. Footnote: explanation of specific entries (placed at the bottom) 7. Source: the origin of the data (placed at the bottom)
Question 2
Distinguish between classification of data and tabular presentation.
| Basis | Classification | Tabular Presentation |
|---|---|---|
| Meaning | Grouping data based on common characteristics | Arranging classified data in rows and columns |
| Purpose | Simplifies raw data | Presents data for easy comparison and analysis |
| Output | Groups or classes | A table with rows and columns |
| Sequence | Comes before tabulation | Comes after classification |
| Example | Grouping students by marks | Table showing number of students in each marks group |
Question 3
Explain the different types of bar diagrams.
1. Simple Bar Diagram: One bar for each category; height represents the value. Used for comparing different categories. Example: Production of different crops.
2. Multiple Bar Diagram: Two or more bars side by side for each category to compare sub-groups. Example: Male and female literacy rates across states.
3. Sub-divided (Component) Bar Diagram: One bar divided into segments representing components of a total. Each segment shows the share of a component. Example: Break-up of government expenditure into defence, education, health.
4. Percentage Bar Diagram: Like sub-divided bar, but each bar shows percentage share of components. All bars are of equal height (100%). Example: Percentage share of different sectors in GDP across years.
Question 4
What is a histogram? How does it differ from a bar diagram?
Difference from bar diagram:
| Basis | Histogram | Bar Diagram |
|---|---|---|
| Data type | Continuous data | Discrete or categorical data |
| Gaps | No gaps between bars | Gaps between bars |
| Width | Width represents class interval | Width is uniform and decorative |
| Construction | Based on frequency distribution | Based on values of categories |
| X-axis | Class limits | Category names |
| Purpose | Shows distribution pattern | Compares values across categories |
Question 5
Construct a pie diagram from the following data:
| Item | Expenditure (Rs) |
|---|---|
| Food | 3000 |
| Clothing | 1000 |
| Rent | 1500 |
| Education | 500 |
| Total | 6000 |
Step 1: Calculate degrees for each item using: Degrees = (Value / Total) × 360°
| Item | Expenditure | Degrees | Calculation |
|---|---|---|---|
| Food | 3000 | 180° | (3000/6000) × 360 = 180° |
| Clothing | 1000 | 60° | (1000/6000) × 360 = 60° |
| Rent | 1500 | 90° | (1500/6000) × 360 = 90° |
| Education | 500 | 30° | (500/6000) × 360 = 30° |
| Total | 6000 | 360° |
Step 2: Draw a circle of convenient radius. Using a protractor, draw sectors of 180°, 60°, 90°, and 30° for Food, Clothing, Rent, and Education respectively. Label each sector.
Question 6
What is an ogive? Explain its types.
Types:
1. Less-than Ogive: Plot upper class limits on the X-axis and less-than cumulative frequencies on the Y-axis. The curve rises from left to right in an S-shape.
2. More-than Ogive: Plot lower class limits on the X-axis and more-than cumulative frequencies on the Y-axis. The curve falls from left to right.
Finding the Median: The point where the less-than ogive and more-than ogive intersect gives the median value. Drop a perpendicular from this intersection point to the X-axis to read the median.
Question 7
Construct a less-than ogive from the following data:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency | 5 | 8 | 12 | 7 | 3 |
Step 1: Calculate less-than cumulative frequencies.
| Marks (Less than) | Cumulative Frequency |
|---|---|
| Less than 10 | 5 |
| Less than 20 | 5 + 8 = 13 |
| Less than 30 | 13 + 12 = 25 |
| Less than 40 | 25 + 7 = 32 |
| Less than 50 | 32 + 3 = 35 |
Step 2: Plot the points (10, 5), (20, 13), (30, 25), (40, 32), (50, 35) on graph paper. Mark X-axis with marks (0 to 50) and Y-axis with cumulative frequency (0 to 35).
Step 3: Join the points with a smooth freehand curve. The resulting S-shaped curve is the less-than ogive.
Question 8
Construct a more-than ogive from the same data (Question 7).
Step 1: Calculate more-than cumulative frequencies.
| Marks (More than) | Cumulative Frequency |
|---|---|
| More than 0 | 5 + 8 + 12 + 7 + 3 = 35 |
| More than 10 | 8 + 12 + 7 + 3 = 30 |
| More than 20 | 12 + 7 + 3 = 22 |
| More than 30 | 7 + 3 = 10 |
| More than 40 | 3 |
Step 2: Plot the points (0, 35), (10, 30), (20, 22), (30, 10), (40, 3) on graph paper.
Step 3: Join the points with a smooth freehand curve. The resulting downward-sloping curve is the more-than ogive.
Question 9
What is a frequency polygon? How is it constructed?
Method 1 (using histogram): 1. Draw the histogram for the frequency distribution. 2. Mark the mid-point of the top of each bar. 3. Join these mid-points with straight lines. 4. Close the polygon by connecting to the mid-points of the previous and next class intervals (with zero frequency).
Method 2 (without histogram): 1. Calculate class mid-points: Mid-point = (Lower + Upper) / 2. 2. Plot mid-points on X-axis and frequencies on Y-axis. 3. Join the points with straight lines. 4. Close the polygon by extending to one class mid-point before and after with zero frequency.
Question 10
Distinguish between a simple bar diagram and a multiple bar diagram.
| Basis | Simple Bar Diagram | Multiple Bar Diagram |
|---|---|---|
| Bars per category | One bar per category | Two or more bars per category |
| Purpose | Compare different categories | Compare sub-groups within each category |
| Example | Production of rice across states | Male and female literacy rates across states |
| Colours | Single colour or shade | Different colours for different sub-groups |
| Legend | Not needed | Required to identify sub-groups |
Question 11
What are the limitations of diagrammatic presentation?
1. Diagrams provide only approximate values — exact figures cannot be read. 2. They are not suitable for precise analysis. 3. They can be misleading if drawn with wrong scales or proportions. 4. They are not a substitute for tables; data may need to be presented in both forms. 5. They require skill and care in construction; a poorly drawn diagram misrepresents data. 6. They are difficult to construct for large data sets.
Question 12
What is an arithmetic line graph? When is it used?
When to use: It is used to show changes in a variable over time. For example, population growth, price trends, production trends, GDP growth. It helps identify trends, cycles, and fluctuations in the data.
Question 13
Explain the rules for constructing a good table.
1. Title: Should be clear, brief, and self-explanatory. 2. Stub and Caption: Row and column headings should be clear and short. 3. Body: Data should be arranged logically — alphabetical, chronological, or size order. 4. Units: Units of measurement should be clearly stated. 5. Totals: Row and column totals should be provided. 6. Footnotes: Should explain abbreviations or exceptional entries. 7. Source: Origin of data should be mentioned. 8. Ruling and Spacing: Proper lines and spacing for clarity. 9. Approximation: Large figures can be rounded off with a headnote. 10. No overload: Table should not be overloaded with too much data.
Question 14
Explain the advantages of diagrammatic presentation of data.
1. Attractive and eye-catching: Diagrams have visual appeal and attract attention. 2. Simple to understand: Even a layperson can interpret diagrams. 3. Comparison is easy: Differences between values are visually apparent. 4. Memorable: Visual impressions last longer than numbers. 5. Reveals trends: Graphs clearly show patterns and trends over time. 6. No need for mathematical knowledge: Simple diagrams can be understood without training. 7. Universal use: Diagrams are used in economics, business, science, and media.
Question 15
What precautions should be taken while drawing diagrams?
1. The diagram should be neat, clean, and properly labelled. 2. The title should be clear and appropriate. 3. The scale should be clearly indicated and proportionate. 4. The diagram should be drawn to scale — no visual distortion. 5. Colours or shades should be used consistently and a legend provided. 6. The source of data should be mentioned. 7. The diagram should not be misleading — avoid 3D effects that distort proportions. 8. Appropriate type of diagram should be chosen for the data. 9. Axes should be clearly labelled with units. 10. The diagram should be simple — avoid unnecessary decoration.
Internal Links
- [Chapter 4 Guide — Presentation of Data](/school/cbse/class/11/economics/cbse-presentation-of-data)
- [All Class 11 Economics Solutions](/school/cbse/class/11/economics/solutions)
- [Class 11 Economics Subject Guide](/school/cbse/class/11/economics)