Chapter 4: Presentation of Data

Economics - Statistics • Class 11

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Chapter Analysis

Intermediate20 pages • English

Quick Summary

The chapter on 'Presentation of Data' discusses various methods and techniques for organizing and presenting data effectively. It covers textual, tabular, and diagrammatic presentations, providing guidelines on when each is appropriate. The importance of using correct types of diagrams, such as bar diagrams, histograms, frequency polygons, and pie charts, is emphasized. It concludes by highlighting how these methods facilitate easier understanding and analysis of data.

Key Topics

  • Textual presentation of data
  • Tabular presentation of data
  • Geometric diagrams: Bar diagram and Pie diagram
  • Frequency diagrams: Histogram and Frequency Polygon
  • Ogives or Cumulative Frequency Curves
  • Arithmetic Line Graph or Time Series Graph

Learning Objectives

  • Understand different forms of data presentation
  • Distinguish between textual, tabular, and diagrammatic presentations
  • Apply appropriate diagram types for varied data sets
  • Interpret graphs and diagrams for statistical analysis
  • Recognize the advantages of different data presentation techniques
  • Develop proficiency in organizing data using tables

Questions in Chapter

1. Bar diagram is a (i) one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above

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2. Data represented through a histogram can help in finding graphically the (i) mean (ii) mode (iii) median (iv) all the above

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3. Ogives can be helpful in locating graphically the (i) mode (ii) mean (iii) median (iv) none of the above

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4. Data represented through arithmetic line graph help in understanding (i) long term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above

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5. Width of bars in a bar diagram need not be equal (True/False).

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6. Width of rectangles in a histogram should essentially be equal (True/False).

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7. Histogram can only be formed with continuous classification of data (True/False).

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8. Histogram and column diagram are the same method of presentation of data. (True/False)

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9. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)

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10. Median of a frequency distribution cannot be known from the ogives. (True/False)

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11. What kind of diagrams are more effective in representing the following? (i) Monthly rainfall in a year (ii) Composition of the population of Delhi by religion (iii) Components of cost in a factory

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12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?

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13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

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Additional Practice Questions

What is the primary difference between a histogram and a bar diagram?

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Answer: A histogram is used to represent continuous data and the bars touch each other, indicating the continuous nature of data. Bar diagrams, however, represent discrete data where bars do not touch each other.

In what situations would you prefer using a pie chart over a bar chart?

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Answer: Pie charts are preferred when you want to show the proportionate part of the whole in categories. They are particularly useful in displaying data that are parts of a total at a single point in time.

How does transforming data into a frequency polygon assist in analysis compared to a histogram?

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Answer: Frequency polygons help in understanding the distribution of data points over intervals, especially useful in comparing different data sets. They simplify the observation of the underlying shape of the data distribution.

Describe the process of creating a time series graph. Why is it useful?

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Answer: To create a time series graph, time intervals are plotted on the x-axis and the variable being measured is plotted on the y-axis. Joining the points over time helps identify trends, periodicity, and fluctuations in the data. They are useful for identifying patterns over a sequence of time.

Explain the advantages of using tabular data presentations.

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Answer: Tabular presentations facilitate the organization of voluminous data for easy comparison and further statistical analysis. They enable efficient display of data relationships across various dimensions and simplify the extraction of information.

What is an ogive and how is it useful in data presentation?

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Answer: An ogive is a plot of cumulative frequency against the class boundaries or midpoints. It helps in estimating the number below a particular value and is useful for identifying the median and quartiles.

Why might one choose a diagrammatic representation over a textual one?

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Answer: Diagrammatic representations allow quicker comprehension and are visually more engaging, enabling the reader to notice trends and make comparisons easily than by reading through text.

How does a frequency curve differ from a frequency polygon?

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Answer: A frequency curve is a smooth curve that passes through the midpoints of the tops of the bars of a histogram or through the points of a frequency polygon. Unlike frequency polygons which have straight lines, frequency curves have smooth lines, providing a better representation of continuous data distribution.

List the steps required to convert discrete data into a histogram.

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Answer: To convert discrete data into a histogram, first place the data into a frequency table, then create intervals, ensuring no gaps between bars, and finally plot the frequencies as touching bars to depict the distribution.

What are some potential pitfalls of using diagrams in data presentation?

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Answer: Common pitfalls include misleading scales, incorrectly labeled axes, distorted perspectives, and over-simplification which can lead to misinterpretation of data.