CBSE Class 11 Economics Presentation of Data

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CHAPTER - 4: PRESENTATION OF DATA

Very short answer questions (1 mark each)

1. Name the different ways of presenting the data. [1 Mark]

Answer:
1. Textual presentation.
2. Tabular presentation.
3. Diagrammatic and graphical presentation.

Teacher's Note:
a) Data presentation is the process of arranging and organizing data so that it can be easily understood.
b) The choice of presentation method depends on the nature of the data and the objective of the study.

2. Define textual presentation of data. [1 Mark]

Answer:
1. Textual presentation involves presenting data in the form of text, paragraphs, or descriptive sentences.
2. It is most suitable when the quantity of data is small and not very extensive.

Teacher's Note:
a) Textual presentation relies heavily on the reader's ability to comprehend written facts.
b) It lacks visual impact compared to tables and graphs.

3. What is meant by tabular presentation of data? [1 Mark]

Answer:
1. Tabular presentation is the systematic organization of classified data in rows and columns.
2. It facilitates comparison and highlights important characteristics of the data at a glance.

Teacher's Note:
a) A table is an orderly arrangement of data highlighting rows and columns.
b) Tabulation simplifies complex data for efficient analysis and interpretation.

4. Define the following: [1 Mark]
a) Simple bar diagram
b) Multiple bar diagram
c) Component/sub divided bar diagram
d) Pie diagram
e) Histogram
f) Frequency polygon
g) Frequency curve
h) Ogive
i) Arithmetic line graph/Time series.

Answer:
1. Simple bar diagram: A set of equidistant bars of equal width representing a single set of numerical data.
2. Multiple bar diagram: A diagram used to compare two or more sets of interrelated data using adjacent bars.
3. Component/sub divided bar diagram: A bar diagram where each bar is divided into several segments to show the total value and its component parts.
4. Pie diagram: A circular chart divided into sectors, where each sector represents the proportion of a specific component to the total.
5. Histogram: A two-dimensional graphical representation of a continuous frequency distribution using adjacent rectangular bars.
6. Frequency polygon: A line graph obtained by joining the midpoints of the top sides of the consecutive rectangles in a histogram.
7. Frequency curve: A smooth, freehand curve drawn through the midpoints of the top of the histogram rectangles representing a frequency distribution.
8. Ogive: A cumulative frequency curve plotted on graph paper to determine the median and partition values.
9. Arithmetic line graph/Time series: A graph showing changes in the values of a variable over successive time periods on an arithmetic scale.

Teacher's Note:
a) Diagrams and graphs provide visual tools for quick comprehension of statistical data.
b) Each diagram type is chosen based on the specific characteristics of the dataset being analyzed.

5. Name the point of intersection between 'less than' and 'more than ogive'. [1 Mark]

Answer:
1. The point of intersection between the less than ogive and more than ogive gives the median of the distribution.

Teacher's Note:
a) The abscissa (x-coordinate) of the intersection point represents the median value.
b) This graphical method is useful for locating partition values without calculation.

Short answer questions (3/4 marks each)

1. Explain different types of classification used in tabulation. [3 Marks]

Answer:
1. Qualitative classification: Classification of data according to attributes or qualities such as literacy, gender, or religion.
2. Quantitative classification: Classification of data according to numerical characteristics or variables such as height, weight, or income.
3. Chronological classification: Classification of data based on time periods such as years, months, or quarters.
4. Spatial classification: Classification of data based on geographical location such as countries, states, or cities.

Teacher's Note:
a) Classification is the primary step in tabulating raw data.
b) Proper classification ensures that data with similar characteristics are grouped together systematically.
c) Always define the basis of classification clearly before tabulating the data.

2. Distinguish between a bar diagram and histogram. [3 Marks]

Answer:

Teacher's Note:
a) Bar diagrams represent categorical data, while histograms represent continuous grouped data.
b) A common mistake is drawing histograms with gaps between bars.
c) Area of rectangles in a histogram matters when class intervals are unequal.

3. Distinguish between 'Frequency polygon' and 'frequency curve'. [3 Marks]

Answer:

Teacher's Note:
a) Both are derived from histograms or frequency distributions.
b) A frequency polygon uses straight lines, whereas a frequency curve uses a smooth contour.
c) The frequency curve provides a clearer picture of the distribution shape for large datasets.

Long answer questions (6 marks each)

1. What are the different parts of a table? Draw a format of a table showing all these parts. [6 Marks]

Answer:
1. Table Number: A unique number assigned to the table for easy reference and identification.
2. Title: A brief and clear description of the contents of the table.
3. Headnote: Information placed below the title to provide additional context, such as units of measurement.
4. Stubs: Row headings that describe the data presented in the horizontal rows.
5. Captions: Column headings that describe the data presented in the vertical columns.
6. Body: The main numeric data enclosed in the cells of the table.
7. Unit of Measurement: Specifies the unit in which figures are expressed.
8. Source Note: Indicates the original source from which the data has been collected.
9. Footnotes: Explanatory notes provided at the bottom of the table for specific items.

Format of a table:

Teacher's Note:
a) A well-structured table must contain all essential components to be self-explanatory.
b) Captions and stubs must be clearly labeled to avoid ambiguity.
c) Source notes are mandatory for secondary data to maintain authenticity.
d) Drawing a clean, properly formatted table layout is crucial for full marks in board exams.

Practical questions (3/4/6 marks each)

1. Present the following data with the help of simple bar diagram [4 Marks]

Answer:
1. Construct a simple bar diagram with years (2006, 2008, 2010, 2012) on the horizontal axis (X-axis).
2. Represent the production of wheat in million tonnes on the vertical axis (Y-axis) with an appropriate scale (e.g., 1 cm = 50 million tonnes).
3. Draw vertical bars of equal width for each year with heights corresponding to 100, 210, 350, and 500 respectively.
4. Leave equal spaces between consecutive bars to complete the simple bar diagram.

Teacher's Note:
a) Ensure the scale on the Y-axis starts from zero and is uniform throughout.
b) Width of all bars and gaps between them must be uniform.
c) Label both axes clearly with units and provide a descriptive title.

2. Represent the following data by a Multiple Bar-Diagram. [4 Marks]

Answer:
1. Use a multiple bar diagram where two adjacent bars are constructed for each year to represent imports and exports side by side.
2. Plot years on the X-axis and monetary values in billion Rs. on the Y-axis using a suitable scale.
3. Use different shades, colors, or patterns to distinguish between import bars and export bars.
4. Include an index or legend explaining the shading or colors used for imports and exports.

Teacher's Note:
a) Multiple bar diagrams are used for comparing two or more sets of interrelated data series.
b) Bars within a group must touch each other without any gap, while space is maintained between different year groups.
c) Accuracy in plotting decimal values like 478.50 and 440.40 on the Y-axis is essential.

3. Represent the following data by a component bar-diagram. [4 Marks]

Average weekly earnings (Rs.) in all industries.

Answer:
1. Calculate the cumulative totals or segments for each bar: for 2010, the bar height is 200, divided into segments of 137.5 (Men) and 62.5 (Women).
2. Similarly for 2011: total height 260, divided into 151.5 and 108.5.
3. For 2012: total height 280, divided into 165 and 115.
4. For 2013: total height 300, divided into 174.5 and 125.5.
5. For 2014: total height 325, divided into 188 and 137.
6. For 2015: total height 330, divided into 205 and 125.
7. Plot years on the X-axis and earnings on the Y-axis, stacking the components within each bar and providing an index.

Teacher's Note:
a) Component bar diagrams show both total magnitude and the relative contribution of parts.
b) The base component (Men) is placed at the bottom, and the next component (Women) is stacked on top of it.
c) Different shadings or patterns must be used for men's and women's earnings with a clear legend.
d) Verify that the sum of components matches the given total for every year.

4. The following table shows the monthly expenditure of two families. Represent the data by a percentage sub-divided bar diagrams. [5 Marks]

Answer:

[Figure: Two vertical bar diagrams of equal height 100 units representing Family A and Family B, divided into segments proportional to the cumulative percentage values of each expense item]

Teacher's Note:
a) Percentage sub-divided bar diagrams convert absolute values into percentages so that totals for all bars equal 100.
b) Cumulative percentages are calculated to mark the dividing lines for each component inside the bars.
c) This type of diagram is best used to compare the relative composition of different totals.
d) Always ensure the bar height is uniformly scaled to 100 percent.

5. In 2004 - 2005, National Income of India according to the industry of origin (at 2000 - 2001 prices) was as given below. Present this information in the form of a Pie diagram. [5 Marks]

Answer:

[Figure: A circle divided into sectors with central angles 144°, 75.6°, 68.4°, 46.8°, and 25.2° representing Agriculture, Industry, Transport, Administration, and Banking respectively]

Teacher's Note:
a) The central angle of each sector is calculated using the formula Component Value / Total Value × 360°.
b) The sum of all central angles must equal exactly 360° to ensure accuracy.
c) Sectors are drawn in descending order or clockwise starting from the 12 o'clock position in standard practice.
d) Pie diagrams effectively show percentage breakdowns of a total aggregate.

6. Draw a histogram and frequency polygon to represent the following data: [5 Marks]

Answer:

[Figure: A histogram with contiguous rectangular bars for each class interval on the X-axis and frequencies on the Y-axis, overlaid with a frequency polygon connecting the mid-points of the top of each bar]

Teacher's Note:
a) A histogram requires continuous class intervals and has no gaps between bars.
b) The frequency polygon is constructed by joining the mid-points of the top of each histogram rectangle with straight line segments.
c) To close the frequency polygon on the base axis, imaginary classes at -5 to 0 and 80 to 85 with zero frequency are assumed.
d) Area under the frequency polygon equals the area of the histogram.

7. Represent the following data by means of Histogram [5 Marks]

Answer:

[Figure: A histogram showing adjusted frequencies for unequal class intervals on the Y-axis against capital ranges on the X-axis]

Teacher's Note:
a) When class intervals are unequal, frequencies must be adjusted relative to the lowest or standard class width.
b) Adjusted frequency formula = (Given Frequency / Width of that Class) × Lowest Class Width.
c) Notice the overlapping interval 30 - 50 and 40 - 50 as printed in the question data table.
d) Heights of the histogram bars represent frequency densities rather than absolute frequencies when widths vary.

8. Present the following data in the form of a histogram and frequency polygon. [5 Marks]

Answer:

[Figure: A histogram for marks starting from 10 to 70 with uniform class width 10, combined with a frequency polygon passing through the midpoints]

Teacher's Note:
a) The distribution starts directly at 10, so a kink or break mark is used on the X-axis between 0 and 10.
b) All class intervals are equal (width = 10), so no frequency adjustment is necessary.
c) The frequency polygon is extended to touch the X-axis at midpoints 5 and 75 to complete the enclosed area.
d) Histograms provide a visual representation of the mode directly from the highest bar.

9. Draw Histogram and Frequency curve from the following figures. [4 Marks]

Answer:

[Figure: Histogram and frequency curve drawn with Length of leaves on the X-axis and No. of leaves on the Y-axis. The class intervals are continuous from 6.5 to 13.5. Rectangles are constructed for each class with heights corresponding to the frequencies (5, 12, 25, 48, 32, 6, 1). A frequency curve is smoothly joined through the midpoints of the top of each rectangle.]

Teacher's Note:
a) Ensure class intervals are continuous before plotting the histogram.
b) The frequency curve is obtained by joining the mid-points of the top of each rectangle with a freehand smooth curve.
c) The Y-axis starts from zero to maintain graphical accuracy.
d) Area of each rectangle is proportional to the respective frequency.

10. Draw a less than ogive and more than from the following data: [4 Marks]

Answer:

1. Prepare cumulative frequency tables for less than and more than series.
2. Less than cumulative frequencies: 7, 22, 57, 85, 95.
3. More than cumulative frequencies: 95, 88, 73, 38, 10.
4. Plot upper class limits against less than frequencies for the less than ogive, and lower class limits against more than frequencies for the more than ogive.
5. [Figure: Less than ogive (rising curve) and more than ogive (falling curve) plotted on the same graph intersecting at the median value.]

Teacher's Note:
a) Less than ogive uses upper limits and cumulates frequencies from top to bottom.
b) More than ogive uses lower limits and cumulates frequencies from bottom to top.
c) The intersection point of both ogives determines the median graphically.
d) Scale on both axes must be clearly marked and uniform.

11. Represent the following data of annual profits of a firm with help of a time series graph. [4 Marks]

Answer:

1. Take Years on the horizontal X-axis at equal intervals.
2. Take Profits in Rs. crores on the vertical Y-axis.
3. Plot the points for each year (2007, 60), (2008, 72), (2009, 75), (2010, 65), (2011, 80), (2012, 95).
4. Join the plotted points with straight line segments to form a line graph.
5. [Figure: Line graph showing upward and downward trends of annual profits from 2007 to 2012.]

Teacher's Note:
a) Time series graphs represent changes in values over a period of time.
b) Time is always plotted on the X-axis.
c) Connecting consecutive points shows the trend clearly.
d) A kink mark on the Y-axis can be used if the scale does not start at zero, though here it starts from 0 or 50.

12. Present the following data graphically [4 Marks]

Answer:

1. Represent the data using a multiple bar diagram or a double line graph with Years on the X-axis and values in crores on the Y-axis.
2. For each year, plot two adjacent bars or points, one for Imports and one for Exports.
3. Use different shades or colors to distinguish between Imports and Exports along with an index.
4. [Figure: Multiple bar diagram / Double time series graph comparing Imports and Exports from 2005-06 to 2009-10.]

Teacher's Note:
a) Multiple bar diagrams are used to compare two or more sets of data related to the same time period.
b) Proper labeling and an index/legend are mandatory.
c) Values grow exponentially, so a suitable scale must be chosen.
d) Double line graphs are equally effective for time series comparison of two variables.

NCERT text book questions

1. Answer the following questions, 1 to 10, choosing the correct answer
a) Bar diagram is a [1 Mark]
(i) One-dimensional diagram
(ii) Two-dimensional diagram
(iii) Diagram with no dimension
(iv) None of the above

Answer: (i) One-dimensional diagram

1. Bar diagrams take only length into account while width is kept arbitrary.
2. Hence, bar diagrams are one-dimensional diagrams.
3. Correct option is (i).

Teacher's Note:
a) Length represents magnitude in bar diagrams.
b) Watch out for confusion with two-dimensional diagrams like pie charts or squares.

b) Data represented through a histogram can help in finding graphically the [1 Mark]
(i) Mean
(ii) Mode
(iii) Median
(iv) All the above

Answer: (ii) Mode

1. Mode of a frequency distribution can be located graphically using a histogram.
2. Correct option is (ii).

Teacher's Note:
a) Mode is found by drawing cross lines from adjacent rectangles to the highest rectangle.
b) Median is located using ogives, not histograms.

c) Ogives can be helpful in locating graphically the [1 Mark]
(i) Mode
(ii) Mean
(iii) Median
(iv) None of the above

Answer: (iii) Median

1. Less than and more than ogives intersect at the median point.
2. Correct option is (iii).

Teacher's Note:
a) Ogives are cumulative frequency curves.
b) The abscissa of the intersection point gives the median.

d) Width of bars in a bar diagram need not be equal (True/False). [1 Mark]

Answer: False

1. All bars in a bar diagram must be of uniform and equal width for aesthetic and comparative clarity.
2. Hence, the statement is False.

Teacher's Note:
a) Uniform width ensures visual balance in bar charts.
b) Only heights vary according to the magnitude.

e) Width of rectangles in a histogram should essentially be equal (True/ False). [1 Mark]

Answer: False

1. Class intervals in a frequency distribution can be unequal, leading to rectangles of varying widths.
2. Hence, the statement is False.

Teacher's Note:
a) When class intervals are unequal, heights are adjusted proportionately (frequency density).
b) Rectangles do not necessarily have equal widths.

f) Histogram can only be formed with continuous classification of data (True/False). [1 Mark]

Answer: True

1. Histograms require continuous class intervals so that adjacent rectangles touch each other without gaps.
2. Hence, the statement is True.

Teacher's Note:
a) Discontinuous data must be converted to continuous data before plotting a histogram.
b) Gaps between bars are characteristic of bar diagrams, not histograms.

g) Mode of a frequency distribution can be known graphically with the help of histogram. (True/False). [1 Mark]

Answer: True

1. Mode is graphically located at the peak of the histogram using cross-diagonal lines.
2. Hence, the statement is True.

Teacher's Note:
a) This is a standard graphical method for estimating mode.
b) It requires continuous frequency distributions.

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