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Class 11 Commerce

Economics – Statistics for Economics

Presentation of Data

Presentation of Data

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Study Action Plan (Sorted by Difficulty)
Arithmetic Line Graph
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High
Bar Diagrams
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Diagrammatic Presentation of Data
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Frequency Polygon
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Histogram
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Ogive
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Pie Diagrams
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Tabular Presentation of Data
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Textual Presentation of Data
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High

Learning Objectives

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Learning Objectives

  • Present data using tables.
  • Represent data using appropriate diagrams.
  • Understand the parts of a good statistical table.
  • Classify data into qualitative, quantitative, temporal, and spatial categories.
  • Construct various types of diagrams for data presentation.

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Revision Notes & Summary

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Presentation of Data

1. Introduction

  • Data needs to be presented in a compact and comprehensible form.
  • Three forms of data presentation:
    • Textual or Descriptive
    • Tabular
    • Diagrammatic

2. Tabular Presentation of Data

  • A table organizes data in rows and columns.
  • Essential parts of a good statistical table:
    1. Table Number: Identifies the table (e.g., Table 4.5).
    2. Title: Clear and brief description of the table's content.
    3. Captions/Column Headings: Designations at the top of each column.
    4. Stubs/Row Headings: Designations for each row.
    5. Body of the Table: Contains actual data.
    6. Unit of Measurement: States the unit of the figures presented.
    7. Source: Indicates where the data is obtained.
    8. Note: Explains specific features of the data that are not self-explanatory.

Example Table

LocationMale (Rural)Female (Rural)Total (Rural)
India795968

3. Diagrammatic Presentation of Data

  • Provides quick understanding of data.
  • Types of diagrams:
    • Geometric Diagrams: Bar and pie diagrams.
    • Frequency Diagrams: Show frequency distributions.
    • Arithmetic Line Graphs: Used for time series data.

Bar Diagrams

  • Simple Bar Diagram: Compares single sets of data.
  • Multiple Bar Diagram: Compares two or more sets of data.
  • Component Bar Diagram: Shows parts of a whole.

Pie Diagrams

  • Represents data as a circle divided into proportional segments.

4. Activities

  • Construct a table presenting data collected from students.
  • Draw a bar diagram for the number of students in each class.
  • Represent data using a component bar diagram or pie chart.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

It is arbitrary and does not affect the representation.

B.

It represents the frequency of the class interval.

C.

It is as important as the height for accurate representation.

D.

It is used to calculate the median of the data.
Correct Answer: C

Solution:

In a histogram, both the width and height of the rectangles are important for accurately representing the data.

Chapter Concept:

Diagrammatic Presentation of Data

A.

Arithmetic Line Graph

B.

Bar Diagram

C.

Pie Diagram

D.

Frequency Polygon
Correct Answer: A

Solution:

Arithmetic line graphs are best suited for displaying trends over time as they plot data points over a time interval, showing changes and trends clearly.

Chapter Concept:

Diagrammatic Presentation of Data

A.

Tabular presentation

B.

Textual presentation

C.

Diagrammatic presentation

D.

None of the above
Correct Answer: B

Solution:

Textual presentation is effective for emphasizing specific points, such as the number of schools closed during a strike, especially when the dataset is small.

Chapter Concept:

Textual Presentation of Data

A.

Histograms can be used for both discrete and continuous data

B.

Histograms are used to find the mean of a data set

C.

Histograms are useful for identifying the mode of a frequency distribution

D.

Histograms display data in a pie chart format
Correct Answer: C

Solution:

Histograms are useful for identifying the mode of a frequency distribution graphically.

Chapter Concept:

Histogram

A.

When comparing two or more distributions on the same axes.

B.

When presenting data with unequal class intervals.

C.

When data is categorical and not numerical.

D.

When data needs to be represented in a circular format.
Correct Answer: A

Solution:

A frequency polygon is more useful than a histogram when comparing two or more distributions plotted on the same axes.

Chapter Concept:

Frequency Polygon

A.

It provides more detailed data

B.

It is more visually appealing

C.

It allows for quicker comprehension

D.

It is more accurate
Correct Answer: C

Solution:

Bar diagrams translate abstract data into a visual format, making it easier and quicker to comprehend compared to textual data.

Chapter Concept:

Bar Diagrams

A.

The tallest rectangle in the histogram.

B.

The width of the rectangles.

C.

The cumulative frequency curve.

D.

The area under the histogram.
Correct Answer: A

Solution:

The mode of a frequency distribution can be graphically determined by the tallest rectangle in a histogram, which represents the most frequent class interval.

Chapter Concept:

Histogram

A.

When data needs to be visually compared.

B.

When data is voluminous and requires compact presentation.

C.

When highlighting specific details within a small dataset.

D.

When statistical analysis is required.
Correct Answer: C

Solution:

Textual presentation is effective for small datasets where specific details need to be highlighted.

Chapter Concept:

Textual Presentation of Data

A.

To determine the mode of a distribution

B.

To calculate the mean of a dataset

C.

To find the median of a frequency distribution

D.

To identify the range of data
Correct Answer: C

Solution:

An ogive is a cumulative frequency curve used to determine the median of a frequency distribution.

Chapter Concept:

Ogive

A.

Connect the plotted points with straight lines.

B.

Use class boundaries instead of midpoints for plotting.

C.

Ensure the class intervals are unequal.

D.

Plot cumulative frequencies instead of simple frequencies.
Correct Answer: A

Solution:

To construct a frequency polygon, points are plotted at the midpoints of the tops of the rectangles of a histogram and connected with straight lines. This ensures the polygon accurately represents the frequency distribution.

Chapter Concept:

Frequency Polygon

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Presentation of Data

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True or False

Correct Answer: True

Solution:

A histogram is indeed a two-dimensional diagram where rectangles represent frequency distributions for continuous data.

Chapter Concept :

Histogram

Correct Answer: True

Solution:

Ogives, which are cumulative frequency curves, can be used to determine the median by finding the point where the 'less than' and 'more than' ogives intersect.

Chapter Concept :

Ogive

Correct Answer: False

Solution:

A histogram is a two-dimensional diagram, not one-dimensional, as it uses rectangles to represent frequency distributions.

Chapter Concept :

Histogram

Correct Answer: True

Solution:

Bar diagrams are suitable both for frequency type and non-frequency type variables and attributes. However, they are more convenient for non-frequency data such as income-expenditure profiles, export/imports over the years, etc.

Chapter Concept :

Bar Diagrams

Correct Answer: False

Solution:

A good statistical table should include the source of data to provide context and credibility to the information presented.

Chapter Concept :

Tabular Presentation of Data

Correct Answer: True

Solution:

Tabular presentation is a method of organizing data into rows and columns, which helps in making the data clear and ready for further statistical analysis.

Chapter Concept :

Tabular Presentation of Data

Correct Answer: False

Solution:

Textual presentation of data is more suitable for smaller datasets, as larger datasets can become cumbersome to comprehend in text form.

Chapter Concept :

Textual Presentation of Data

Correct Answer: True

Solution:

Diagrammatic presentation translates abstract data into more concrete forms, making it quicker to comprehend, though it may lack the precision of tabular data.

Chapter Concept :

Diagrammatic Presentation of Data

Correct Answer: True

Solution:

Pie diagrams represent data proportions and require absolute values to be converted into percentages to accurately reflect the size of each sector in the circle.

Chapter Concept :

Pie Diagrams

Correct Answer: True

Solution:

Component bar diagrams, also called sub-diagrams, are very useful in comparing the sizes of different component parts and for highlighting the relationship among these integral parts.

Chapter Concept :

Bar Diagrams

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