# NCERT Solutions for Class 8 Maths Chapter 5 Data Handling (EX 5.1) Exercise 5.1

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, Chapter 5. The concept of raw data is covered in data handling, along with how it is represented using bar graphs, double bar graphs, and frequency distribution charts. While studying grouped frequency distribution, the students will become familiar with words like class intervals and upper and lower class bounds.

Mathematical concepts may be used by students to address difficulties in the real world. Every industry uses Mathematics in some capacity. A Mathematical background may be advantageous for a variety of vocations. By using the concepts they learn in this course, students can pursue careers in astronomy, astrophysics, statistics, weather forecasting, and other related fields. One of the program’s core courses, Mathematics, is taught in school starting in the first grade. A learner’s whole growth hinges on their ability to comprehend the basics of Mathematics. The branch of Mathematics known as statistics looks at how to extract useful information. It might also be referred to as the collection of data about many aspects of people’s lives that is useful to the state. Information on different data displays, including frequency distribution, is provided in this chapter. Students learn how to visualize data using a variety of graphs in this chapter, including bar graphs, histograms, frequency polygons, etc. To find the central tendency, the chapter also teaches students how to compute the mean, median, and mode of the raw data.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, also introduces histograms, a graphical method of expressing data. Each bar’s height in this example represents the frequency of the class interval. Because there are no gaps in the class intervals, unlike a bar graph, there are no spaces between the bars in a histogram. There are five straightforward problems in the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. Students are required to create a frequency distribution chart, histogram, and bar graph using the provided data.

Students must become quite familiar with the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, includes application examples in addition to comprehensive explanations of all concepts and themes. In the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, students may practice the questions after each chapter in a simple manner. If students utilize the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, they will be able to respond to problems more swiftly and correctly.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1  is a useful choice that can be obtained on the Extramarks website or mobile application, although students have access to a broad variety of study materials.

## H2 – NCERT Solutions for Class 8 Maths Chapter 5 Data Handling (EX 5.1) Exercise 5.1

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, can help students gain better theoretical and practical knowledge. The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 is available as a PDF download and addresses every problem from NCERT Class 8 Maths Chapter 5 Exercise 5.1. There are tips and tricks in addition to the answers. That would be beneficial for resolving queries. On Extramarks, the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, are accessible in PDF format.

### H2 – Access NCERT Solutions for Class 8 Chapter 5 – Data Handling

Students can download all the chapter exercises and the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. These solutions are created by experienced teachers and are based on the standards in the CBSE NCERT textbooks. Students may review the complete curriculum and earn better scores by using the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1.

### H3 – NCERT Solutions for Class 8 Maths Chapter 5 Data Handling – Chapter Overview

Data management is important for students to learn since it prepares them for dealing with real-world issues. Additionally, it sharpens their critical-thinking skills and puts their capacity for logic to the test. When processing data, pupils are taught how to categorize the information.

There is a focus on the following in particular in Exercise 5.1 of the chapter:

Graphical representation of data via

Pictograph

A pictogram, often referred to as a pictograph in Mathematics, is a visual representation of data that uses pictures, icons, or other symbols. Using a pictograph, students can depict the frequency of data using pertinent symbols or images. One of the easiest methods to portray data is through pictographs.

Bar graph

A bar graph is a particular type of data visualization that uses rectangular bars, with each bar’s length proportionate to the value it represents. It uses bars of various heights to graphically portray the data. Bar graphs are a frequent way to display business data in real life.

Double bar graph

A double bar graph resembles a standard bar graph in appearance. It only differs in that it compares two data groupings. Because they employ two bars next to each other at different heights to display information, double bars are also known as double bar charts. According to the situation, the bars can be set up either vertically or horizontally.

Organizing data

Since it involves gathering data sets, ensuring security, and preserving research data, organizing data is regarded as one of the most crucial statistical issues. This data consists of a collection of numerical values that are used to analyse the relevant set or sets of data. Graphs are a visual representation of data management. For a better understanding, let’s study more about this intriguing concept, the many graphs employed, and solve a few cases.

Grouping data

Grouping the data is important when working with huge volumes of data. This information can also be shown visually using a bar graph or pictogram. A frequency distribution table of these groups of observations is an effective method for summarizing or analyzing grouped data. Grouped data are those that are produced by grouping individual observations of a variable.

Frequency distribution table

The frequency of each data set is categorized and shown in a frequency distribution table. It lets us evaluate the data using measures of central tendency and variance and aids in the discovery of patterns in the data. Making a frequency distribution table out of the gathered data is the first thing a Mathematician does with it. Calculations, statistical tests, and analyses are all performed afterwards.

Histogram

A histogram is a diagram that shows how data is distributed. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous areas use statistics, which is a branch of Mathematics. Frequency, which may be shown as a table and is known as frequency distribution, is the repeating of numerals in statistical data.

The sums are all resolved precisely as they should be in the test according to the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. Students will make the most of their time and effort as a result. Students who use the Class 8 Maths Exercise 5.1 Solutions are more effective and achieve better outcomes.

Even if these problems have practical implications, students still need to brush up on the strategies that will enable them to answer these questions quickly. Because of this, they require thorough comprehension of many topics as well as quick approaches to complete them within the allotted time. The most popular test guide is available to them with their NCERT Solutions for Class 8 Maths Chapter 5 Data Handling, which will assist students in learning more about it.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, provides an analysis and explanation of each problem from the Class 8 NCERT textbook. The solutions are offered in detail to make sure that students can understand each concept as they work through it. The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 is created by some of the sharpest experts on the Extramarks platform.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, would be very helpful to students preparing for Olympiads, state or national competitive exams, and CBSE exams. The CBSE examinations are based on the NCERT textbooks’ outline. Additionally, students may prepare for tests by using the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1.

### H3 – Here is a Brief Explanation of Every Question Included in this Chapter.

NCERT Class 8 Maths Chapter 5 Exercise 5.1  Question 1

In the first question, students are given four assertions and asked to choose which one(s) a histogram should be drawn under.

Students can learn how to respond to these questions from the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. They have a step-by-step tutorial that will help them understand histograms and how to design them.

Question 2 of Class 8 Maths Chapter 5 Exercise 5.1

The second question provides students with the raw data from which they must, using tally marks, determine the frequency of each characteristic. After that, students must also create a bar graph.

For better comprehension, the Extramarks experts have included step-by-step instructions and detailed explanations for each step in NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 Data Handling.

Question 3 of NCERT Class 8 Maths Chapter 5 Exercise 5.1

Although question 3 first may resemble question 2 in appearance, students must realize that the raw data provided is required to be expressed in equal intervals.

Students can learn how to create these tables from the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1.

Question 4 of NCERT Class 8 Maths Chapter 5 Exercise 5.1

Students are asked to create a histogram in question 4 using the information from question 3’s data.

One must thus be able to extract the same information from the supplied data.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, Data Handling, includes step-by-step instructions to help students arrive at the right conclusion as quickly as possible. Since experts created these answers to NCERT Class 8 Maths Chapter 5 Exercise 5.1, students can expect to get the best possible study materials for their use.

Question 5 of Class 8 Maths Chapter 5 Exercise 5.1

The last exercise question has a graph that contains

number of students

Total number of television hours watched

on the X- and Y-axes plotted. Although the question includes three components, these are the ones that are most frequently chosen to be on test papers. Examine the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, to learn the specifics on how to respond to these queries. Use the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 to be ready for their forthcoming test.

### H3 – NCERT Solutions for Class 8

NCERT Solutions for Class 8 is an extremely important study guide since it helps students establish a strong foundation for their higher levels. There is no need to get overly anxious or overwhelmed, though. NCERT Books are the finest source of study material for Class 8 students. All the principles that a student in Class 8 has to understand are clerly and effectively explained in the textbook.

Students in class 8 should be well-versed in the solutions to the problems in the NCERT textbook. Anyone may refer to the Class 8 Math and Science NCERT Solutions here. Every question in each chapter of maths and science has a thorough solution supplied by the Extramarks, and they are incredibly precise. The answers and in-depth explanations are created by subject-matter experts after considerable study to provide students with a reliable and acceptable source of NCERT solutions. Students will be able to swiftly and easily learn the ideas by using the answers for Class 8 NCERT Science and Math. If students carefully study these NCERT Solutions, they can quickly clear up all of their doubts.

Science and maths are two areas that should take priority in a student’s academic programme. Therefore, it is crucial to emphasize practising the problems and solutions to fully grasp any topics in the relevant chapters if they want to achieve excellent grades and advance in their chosen job. Students can practice the questions and answers based on the Class 8 CBSE Syllabus by consulting the NCERT Books for Class 8 for more practice.

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NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 tips:

Before beginning the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 problems, students should be familiar with the principles of data, how to obtain it, and its representation methods. They must have previously taken classes where they learned how to tabulate data into different types of tables, charts, and graphs. For a deeper comprehension of the ideas covered in this chapter, they might review it once again.

In the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1, students must first practice the examples in Class 8 Maths Chapter 5 Exercise 5.1 to understand the principles and logic. They will feel more certain as a result when answering the exercise questions.

Q.1 For which of these would you use a histogram to show the data?

(a) The number of letters for different areas in a postman’s bag.

(b) The height of competitors in an athletics meet.

(c) The number of cassettes produced by 5 companies.

(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station. Give reasons for each.

Ans

1. The number of letters for different areas in a postman’s bag: Here, we cannot use the histogram as we do not know about the number of letters of different areas. Therefore, we can’t divide the given data into class intervals.
2. The height of competitors in an athletics meet:

Here, a histogram can be drawn as the given data can be divided into class intervals.

1. The number of cassettes produced by 5 companies: As we are not aware about the number of cassettes produced by the given companies, so we cannot divide the data into class intervals. Therefore, a histogram can’t be drawn.
2. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station: The histogram can be drawn here as the given data can be divided into class intervals.

Q.2 The shoppers who come to a departmental store are marked as: man (M), woman(W), boy (B) or girl (G). The following list gives 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 W M W G W M G W M M B G G W

Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Ans

The frequency distribution table is as follows:

$\begin{array}{|ccc|}\hline \mathrm{Shopper}& \mathrm{Tally}\text{ }\mathrm{marks}& \mathrm{Number}\\ \mathrm{W}& \overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\mathrm{lll}& 28\\ \mathrm{M}& \overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}& 15\\ \mathrm{B}& \overline{)\mathrm{llll}}& 5\\ \mathrm{G}& \overline{)\mathrm{llll}}\text{ }\overline{)\mathrm{llll}}\text{ }\mathrm{ll}& 12\\ \hline\end{array}$

The bar graph is as follows: Q.3 The weekly wages (in Rs) 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.

Ans

The frequency distribution table is as follows:

 $\begin{array}{l}\text{ }\mathrm{Interval}\\ 800-810\\ 810-820\\ 820-830\\ 830-840\\ 840-850\\ 850-860\\ 860-870\\ 870-880\\ 880-890\\ 890-900\end{array}$ $\begin{array}{l}\mathrm{Tally}\text{ }\mathrm{marks}\\ \text{ }\mathrm{lll}\\ \text{ }\mathrm{ll}\\ \text{ }\mathrm{l}\\ \text{ }\overline{)\mathrm{llll}}\mathrm{llll}\\ \text{ }\overline{)\mathrm{llll}}\\ \text{ }\mathrm{l}\\ \text{ }\mathrm{lll}\\ \text{ }\mathrm{l}\\ \text{ }\mathrm{l}\\ \text{ }\mathrm{lll}\end{array}$ $\begin{array}{l}\mathrm{Frequency}\\ \text{ }3\\ \text{ }2\\ \text{ }1\\ \text{ }9\\ \text{ }5\\ \text{ }1\\ \text{ }3\\ \text{ }1\\ \text{ }1\\ \text{ }4\end{array}$

Q.4 Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions.

(i) Which group has the maximum number of workers?

(ii) How many workers earn Rs 850 and more?

(iii) How many workers earn less than Rs 850?

Ans

Histogram is as follows: (i) The maximum number of workers is in the group 830 − 840.

(ii) From the graph, we can observe that the workers who earn more than Rs 850 falls in the group of 850 − 860 or 860 − 870 or 870 − 880 or 880 − 890.

Hence, the total number of workers earning more than 850 = 1 + 3 + 1 + 1 + 4 = 10

(iii) It is clear from the graph that the workers who earn less than Rs 850 falls in the group of 800 − 810 or 810 − 820 or 820 − 830 or 830 − 840 or 840 − 850.

Hence, the total number of workers earning less than 850 = 3 + 2 + 1 + 9 + 5 = 20

Q.5 The number of hours for which students of a particular class watched television during holidays is shown through the given graph.

1. For how many hours did the maximum number of students watch TV?
2. How many students watched TV for less than 4 hours?
3. How many students spent more than 5 hours in watching TV? Ans

(i)The maximum number of students watched TV for 4 − 5 hours.

(ii) The students who watched TV for less than 4 hours falls in the group of 1 − 2 hours or 2 − 3 hours or 3 − 4 hours.

Hence, total number of students who watched TV for less than 4 hours

= 4 + 8 + 22

= 34

(iii) The students who watched TV for more than 5 hours falls in the group of 5 − 6 hours or 6 − 7 hours.

Hence, total number of students who watched TV for more than 5 hours

= 8 + 6

= 14

## 1. What are the important concepts discussed in the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1?

There are lots of Data handling concepts discussed in the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1. Some of them are following

Data presented graphically

Pictograph: Symbolic visual representation of data

A bar graph is a visual representation of data that uses uniformly spaced bars whose heights are proportionate to the values they represent.

Double bar graph

A bar graph that concurrently displays two sets of data.

Gathering data

Using a frequency distribution table, organize the data.

Organizing Data

employing a grouped frequency distribution to group data.

## 2. How many problems are there in the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1?

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1  Data Handling has 5 problems. This practice consists of 5 Main Questions. There are sub-questions in the first, fourth, and fifth questions that are all concerned with the representation of data. Data Handling Class 8 Exercise 5.1 covers three key ideas.

Pictograph

Bar graph

Double bar graph

Organizing data

Grouping data

Frequency distribution table

Histogram, etc.

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 provides clear definitions of the aforementioned ideas. The Extramarks website offers students a PDF copy of the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1.

## 3. Is it required to practice all the NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 Questions?

The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 thoroughly outlines the qualities of triangles and their congruency. Students can comprehend this topic better by working through all the straightforward problems in these solutions. The NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.1 will also help students learn with greater enthusiasm and aptitude.