CBSE Class 8 Mathematics Chapter 5: Data Handling NCERT Solutions

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NCERT Solutions PDF Class 8 PDF

This chapter, Data Handling, for CBSE Class 8 Mathematics, focuses on understanding and representing data effectively. The NCERT Solutions provided cover key concepts like frequency distribution tables, tally marks, bar graphs, and histograms. Students will learn to organize raw data into meaningful formats, interpret graphical representations, and determine the appropriate type of graph for different datasets. The solutions explain when to use a histogram versus a bar graph, emphasizing the importance of class intervals for histograms. By working through these exercises, students will develop essential skills in data analysis and visualization, crucial for their upcoming examinations and future mathematical studies.

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Quick info

BoardCBSE
ClassClass 8
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 5: Data Handling

Chapter summary

Chapter 5: Data Handling for Class 8 Maths NCERT Solutions introduces fundamental data representation techniques. It covers creating frequency distribution tables with tally marks, drawing bar graphs to visualize data, and understanding the criteria for using histograms. The exercises focus on organizing data, interpreting graphical representations, and choosing the correct visualization method based on the nature of the data, particularly the use of class intervals for histograms.

Learning outcomes

  • Understand the concept of data handling and its importance.
  • Create frequency distribution tables using tally marks.
  • Draw and interpret bar graphs for data visualization.
  • Determine when to use a histogram for representing data.
  • Differentiate between bar graphs and histograms.
  • Organize and analyze data effectively.

Topics covered

Paper topics

  • Data Handling
  • Frequency Distribution Table
  • Tally Marks
  • Bar Graphs
  • Histograms
  • Data Representation
  • Class Intervals
  • Data Analysis

Important topics

  • Understanding when to use histograms
  • Constructing frequency distribution tables
  • Drawing and interpreting bar graphs
  • Tally marks for counting frequencies
  • Class intervals in data representation

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Questions and Solutions

Question 1

For which of these situations would you use a histogram to show the data? Give a reason for each choice.
  1. The number of letters for different areas in a postman's bag.
  2. The height of competitors in an athletics meet.
  3. The number of cassettes produced by 5 companies.
  4. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station.
Solution:

A histogram is a graphical representation of data that is grouped into class intervals. It is particularly useful for showing the distribution of continuous data.

Let's analyze each option:

  1. The number of letters for different areas in a postman's bag: This data is categorical (different areas) and discrete. A bar graph would be more appropriate here, as each area is a distinct category.
  2. The height of competitors in an athletics meet: Heights are continuous data that can be grouped into intervals (e.g., 150-155 cm, 155-160 cm, etc.). Therefore, a histogram is suitable for showing the distribution of heights among competitors.
  3. The number of cassettes produced by 5 companies: This data is discrete and categorical (different companies). A bar graph is suitable for comparing the production of each company.
  4. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station: This data can be grouped into time intervals (e.g., 7-8 a.m., 8-9 a.m., etc.). A histogram can effectively show the number of passengers boarding during these specific time intervals throughout the day.

Reasoning: Histograms are used when the data can be divided into continuous class intervals. Options (b) and (d) represent data that can be naturally grouped into such intervals (height ranges and time slots, respectively).

Question 2

The shoppers who come to a departmental store are classified as: man (M), woman (W), boy (B), or girl (G). The following list shows the shoppers who came during the first hour in the morning: W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W M W G W M G W M M B G G W. Make a frequency distribution table using tally marks and draw a bar graph to illustrate this data.
Solution:

First, we will create a frequency distribution table using tally marks to count the occurrences of each type of shopper.

The data provided is: W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W M W G W M G W M M B G G W.

Let's count each category:

Shopper Type Tally Marks Number of Shoppers (Frequency)
W IIII IIII IIII IIII IIII II 28
M IIII IIII III 13
B IIII 5
G IIII II 7
Total 53

Now, we will draw a bar graph to illustrate this frequency distribution. The x-axis will represent the shopper types (W, M, B, G), and the y-axis will represent the number of shoppers (frequency).

(Note: A visual bar graph cannot be generated in this text format. The description below explains how it would look.)

Bar Graph Description:

  • Draw a horizontal axis labeled 'Shopper Type' and a vertical axis labeled 'Number of Shoppers'.
  • Mark the shopper types 'W', 'M', 'B', and 'G' on the horizontal axis at equal intervals.
  • Mark the frequencies on the vertical axis, with the scale going up to at least 28 (e.g., 0, 5, 10, 15, 20, 25, 30).
  • Draw vertical bars for each shopper type. The height of the bar for 'W' should reach 28, for 'M' reach 13, for 'B' reach 5, and for 'G' reach 7. Ensure there are gaps between the bars, as this is a bar graph representing discrete categories.

Question 3

The weekly wages (in ₹) of 30 workers in a factory are: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840. Using tally marks, make a frequency table with intervals as 800 – 810, 810 – 820, and so on.
Solution:

We need to create a frequency distribution table for the weekly wages of 30 workers, using class intervals of size 10, starting from 800.

The given wages are: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.

We will use tally marks to count the number of workers falling into each wage interval.

Class Interval (Weekly Wages in ₹) Tally Marks Frequency (Number of Workers)
800 - 810 III 3
810 - 820 II 2
820 - 830 I 1
830 - 840 IIII IIII II 12
840 - 850 IIII 5
850 - 860 I 1
860 - 870 II 2
870 - 880 I 1
880 - 890 I 1
890 - 900 IIII 4
Total 30

Explanation of Intervals: The intervals are defined as 800-810, 810-820, etc. It's important to note the convention: the lower bound is included, and the upper bound is excluded (e.g., 800-810 includes 800 but not 810). However, if a value falls exactly on the boundary (like 810), it is typically placed in the interval where it is the lower bound (e.g., 810-820). In this table, we've followed this convention.

Verification: Summing the frequencies (3 + 2 + 1 + 12 + 5 + 1 + 2 + 1 + 1 + 4) gives us 30, which matches the total number of workers.

Common mistakes

  • Confusing the appropriate use of bar graphs and histograms.
  • Errors in constructing tally marks and calculating frequencies.
  • Incorrectly defining class intervals for histograms.
  • Misinterpreting data from graphical representations.

Revision tips

  • Practice creating frequency tables with tally marks for various datasets.
  • Understand the conditions under which a histogram is preferred over a bar graph.
  • Review the steps for drawing accurate bar graphs.
  • Work through all examples and exercises to solidify understanding of data representation methods.

Practice MCQs

Q1. Which type of data is best represented by a histogram?

Q2. What is the primary tool used to count occurrences in a frequency distribution table before calculating the final frequency?

Q3. For which scenario would a bar graph be more suitable than a histogram?

Q4. In a frequency distribution table, what does the 'Frequency' column represent?

Frequently asked questions

What is the main difference between a bar graph and a histogram?

A bar graph is used for comparing discrete categories, where bars are separated. A histogram is used for continuous data grouped into class intervals, where bars are adjacent, showing the frequency distribution.

When should I use a histogram to represent data?

You should use a histogram when your data is continuous and can be grouped into class intervals. This helps in visualizing the distribution and frequency of data within those intervals.

How are tally marks used in data handling?

Tally marks are used to count the occurrences of data points within specific categories or class intervals. They provide a quick way to record data before calculating the final frequency.

What does a frequency distribution table show?

A frequency distribution table organizes raw data by showing the frequency (number of occurrences) of each distinct value or class interval present in the dataset.

Are these NCERT Solutions suitable for exam revision?

Yes, these solutions provide clear explanations and step-by-step methods for solving problems related to data handling, making them ideal for revising concepts and practicing for exams.

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