CBSE Class 11 Statistics Chapter 4: Presentation of Data - NCERT Solutions

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NCERT Solutions PDF Class 11 PDF

This chapter focuses on the crucial aspect of data presentation in Statistics for Class 11 CBSE students. It covers various graphical methods used to represent data effectively, making complex information understandable. The solutions explain the characteristics and applications of bar diagrams, histograms, arithmetic line graphs, and ogives. Students will learn how each type of diagram is constructed and what kind of data insights it provides, such as identifying trends, modes, or medians. These solutions are designed to clarify the concepts presented in the NCERT textbook, aiding students in grasping the nuances of data visualization and preparing for their examinations by reinforcing theoretical knowledge with practical understanding of graphical representation techniques.

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Quick info

BoardCBSE
ClassClass 11
SubjectStatistics (Economics)
Session2026
LanguageEnglish
TypeNCERT Solutions
Chapter4. Presentation of Data

Chapter summary

Chapter 4, 'Presentation of Data,' delves into the graphical methods for organizing and illustrating statistical data. The NCERT Solutions cover the fundamental types of diagrams like bar diagrams, histograms, and arithmetic line graphs, explaining their construction and utility. It also details the use of ogives for finding the median. The solutions clarify the differences and applications of these visual tools, essential for interpreting statistical information effectively.

Learning outcomes

  • Understand the concept and types of one-dimensional diagrams.
  • Identify the graphical method to find the mode using histograms.
  • Determine the median graphically using ogives.
  • Recognize the utility of arithmetic line graphs for analyzing trends.
  • Differentiate between bar diagrams and histograms regarding bar/rectangle width.
  • Understand the requirement of continuous data for histograms.

Topics covered

Paper topics

  • Bar Diagrams
  • One-dimensional Diagrams
  • Histograms
  • Two-dimensional Diagrams
  • Continuous Classification
  • Arithmetic Line Graphs
  • Time Series Graphs
  • Ogives
  • Cumulative Frequency Curves
  • Graphical determination of Mode
  • Graphical determination of Median
  • Data Presentation

Important topics

  • Bar Diagrams vs. Histograms
  • Graphical determination of Mode using Histograms
  • Graphical determination of Median using Ogives
  • Arithmetic Line Graphs for Trend Analysis
  • Requirement of Continuous Data for Histograms

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Questions and Solutions

Question 1

Bar diagram is a
  1. one-dimensional diagram
  2. two-dimensional diagram
  3. diagram with no dimension
  4. none of the above
Solution:

The correct answer is i. one-dimensional diagram.

Bar diagrams are classified as one-dimensional because their representation relies solely on the height (or length) of the bars, which corresponds to the frequency or value of the variable. The width of the bars and the space between them are kept uniform and do not convey any quantitative information.

Question 2

Data represented through a histogram can help in finding graphically the
  1. mean
  2. mode
  3. median
  4. non-of the above
Solution:

The correct answer is ii. mode.

A histogram is a graphical representation of a frequency distribution using adjacent rectangles. The width of each rectangle represents a class interval, and its height represents the frequency of that interval. The class interval with the tallest rectangle, known as the modal class, is used to graphically estimate the mode of the data distribution.

Question 3

Ogives can be helpful in locating graphically the
  1. mean
  2. mode
  3. median
  4. non-of the above
Solution:

The correct answer is iii. median.

Ogives, also known as cumulative frequency curves, are plotted using cumulative frequencies. By plotting both the 'less than' and 'more than' cumulative frequency curves on the same graph, their point of intersection directly indicates the median of the frequency distribution. The median is the value that divides the data into two equal halves.

Question 4

Data represented through an arithmetic line graph help in understanding

(i) Long term trend

(ii) Cyclicity in data

(iii) seasonality in data

(iv) all the above

Solution:

The correct answer is iv. all the above.

Arithmetic line graphs, commonly referred to as time series graphs, plot data points over a continuous time period. This graphical representation is highly effective for identifying and understanding long-term trends, cyclical patterns (like business cycles), and seasonal variations within the data. Time is typically plotted on the horizontal (X) axis, and the variable's value is plotted on the vertical (Y) axis.

Question 5

State whether the following statements are True or False.

(i) Width of bars in a bar diagram need not to be equal.

(ii) Width of rectangles in a histogram should essentially be equal

(iii) Histogram can only be formed with continuous classification of data.

(iv) Histogram and column diagram are the same method of presentation of data.

(v) Mode of a frequency distribution can be known graphically with the help of a histogram.

(vi) Median of a frequency distribution cannot be known from the ogives.

Solution:

(i) False. In bar diagrams, all bars must be of equal width and should be placed at equal distances from each other to ensure a consistent visual comparison.

(ii) False. The width of rectangles in a histogram is determined by the width of the class intervals. These widths may or may not be equal, depending on whether the class intervals are uniform.

(iii) True. Histograms are constructed for continuous data. If the data is not continuous (e.g., discrete classes), it must first be converted into continuous classes before a histogram can be drawn.

(iv) False. While both use rectangular bars, histograms represent continuous frequency distributions, and the bars are adjacent. Column diagrams are typically used for discrete or categorical data, and bars may have spaces between them.

(v) True. The mode of a frequency distribution can be graphically estimated using a histogram by identifying the tallest rectangle, which corresponds to the modal class.

(vi) False. Ogives (cumulative frequency curves) are specifically used to graphically determine the median of a frequency distribution.

Common mistakes

  • Confusing the properties of bar diagrams and histograms regarding bar/rectangle width.
  • Incorrectly assuming histograms can be used for discrete data without conversion.
  • Misidentifying the graphical method for finding the median (confusing with ogives).
  • Not recognizing that bar diagrams require equal bar widths and equal distances.

Revision tips

  • Focus on the key differences between bar diagrams and histograms, especially regarding width.
  • Practice identifying which graphical tool (histogram, ogive) is used to find specific statistical measures (mode, median).
  • Review the conditions under which histograms are applicable (continuous data).
  • Understand the primary purpose of arithmetic line graphs (trend analysis).

Practice MCQs

Q1. Which type of diagram is considered one-dimensional?

Q2. Graphically, the mode of a frequency distribution is best represented by which diagram?

Q3. What statistical measure can be located graphically using ogives?

Q4. Arithmetic line graphs are primarily used to show:

Q5. For a histogram, the width of the rectangles:

Frequently asked questions

What is the main purpose of Chapter 4: Presentation of Data in Class 11 Statistics?

This chapter teaches students how to visually represent statistical data using various graphical methods like bar diagrams, histograms, ogives, and arithmetic line graphs, making data easier to understand and analyze.

How can a histogram help in finding the mode?

A histogram represents data through adjacent rectangles where the height corresponds to frequency. The modal class (the class with the highest frequency) can be identified, and the mode can be estimated graphically from the histogram.

What are ogives used for in data presentation?

Ogives, or cumulative frequency curves, are used to graphically determine the median of a frequency distribution. The intersection of 'less than' and 'more than' ogives gives the median.

Are bar diagrams and histograms the same?

No, they are different. Bar diagrams are used for categorical data and have equal widths and spaces between bars. Histograms are used for continuous data, have no gaps between rectangles (unless a class frequency is zero), and rectangle widths correspond to class intervals.

What is the significance of arithmetic line graphs?

Arithmetic line graphs, also known as time series graphs, are used to show trends in data over a period of time. They are useful for understanding long-term patterns, seasonality, and cyclicity.

Can histograms be used for discrete data?

Histograms are primarily for continuous data. If data is discrete, the class intervals are first converted into continuous classes before constructing a histogram.

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