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# NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 Statistics - PDF Download

The NCERT solutions for class 9 maths chapter 12 ex 12.1 focuses on graphical representations, which emphasize the various methods of showing the data, such as bar graph, histogram, frequency polygons, etc. Bar graphs are two-dimensional representations of numerical data in which each data point in a dataset is represented by a vertical bar extending from one edge to the other.

Class 9 maths chapter 12 exercise 12.1 NCERT solution for Statistics consists of 9 questions in which some of the questions are asked to present the data in a bar graph, some of them about histogram and some of questions are about frequency polygon. Our subject experts of maths have provided step-by-step answers to all the questions given in NCERT solutions. All the essential concepts associated with the questions have been explained in these solutions. These solutions are the best practice for preparing for CBSE examinations. The best way to strengthen your knowledge is to use NCERT Solutions provided by eSaral. Students should go through these solutions to identify their weak points. You can also download the NCERT class 9 exercise 12.1 in PDF format from the official website of eSaral. It is free to download, so students can use it.

## Topics Covered in Exercise 12.1 Class 9 Mathematics Questions

Chapter 12 of class 9 maths ex 12.1 focuses on fundamental concepts such as Histogram, Bar graph and frequency polygon over graphs, as outlined in terms such as frequency, maximum and minimum values, which are related to each of the questions of the exercise.

 1 Graphical Representation of Data Bar Graphs Histogram  Frequency Polygon
1. Graphical Representation of Data

It is widely accepted that a graphical representation of data is more effective than a thousand words. There are various techniques that can be used to present data in a visually appealing manner.

(A) Bar Graphs - Bar graph is a graphical representation of a variable in which bars of the same width are drawn with the equal spacing.

The value of the variable is shown on the other axis and the bar height represents the value of the variable. This is the simplest way to represent the data as rectangular bars.

• Each bar should be of the same thickness.

• The distance between bars should be the same.

• The bar height should correspond to the numerical value to be represented.

(B) Histogram - It is like a bar graph, but it is used to represent continuous class intervals.

• You need to draw the class intervals on the x-axis.

• The height represents the frequency of the class intervals.

(C) Frequency Polygon - Frequency is another term for describing quantitative data.

To representing data in frequency polygon

• The first step is to draw a histogram.

• Then join the mid-points of the upper sides of the adjacent rectangles of this histogram by means of line segments.

• The middle of the first bar should be connected to the middle of the imaginary interval on the x-axis.

• The middle of the last bar should be connected to the middle of the next interval of the x-axis.

If you want to draw a frequency polygon without using the histogram, you will need to figure out the class mark of each interval first and then use those points to make the frequency a polygon.

To find the class-mark of a class interval, we find the sum of the upper limit and lower limit of a class and divide it by 2.

Class-mark = upper limit + lower limit/ 2

## Tips for Solving Exercise 12.1 Class 9 Chapter 12 Statistics

eSaral’s academic team of mathematics have combined some very useful tips to solve graph questions included in ex 12.1. You can check them below.

1. You can easily solve the questions in NCERT solutions class 9 maths chapter 12 ex 12.1 Statistics if you practice with different types of graphs using the examples given.

2. In order to understand the distinctions between the bar graph, the histogram, and the frequency polygon, students should practice the graph described in the NCERT solutions provided by eSaral’s subject experts.

## Importance of Solving Ex 12.1 Class 9 Maths Chapter 12 Statistics

Solving questions of NCERT solutions for class 9 maths chapter 12 ex12.1 provided by subject experts of eSaral have tremendous benefits and they are very reliable.

1. NCERT solutions for class 9 maths ex 12.1 are created by eSaral, with the aim of helping students and covering all questions including Statistics.

2. All solutions are presented in a comprehensive and sequential manner, allowing students to solve all questions with ease.

3. These solutions are highly precise and detailed, which can assist students in preparing for the examination.

4. NCERT solutions for ex 12.1 class 9 maths are available in PDF format which you can download for future reference.

Question 1. What do you understand by the Bar graph?

Answer 1. Bar graph is a graphical representation of a variable in which bars of the same width are drawn with the equal spacing. Bar graphs are a way of comparing and contrasting different types of data by simply comparing quantities, frequencies, or other measurements.

Question 2. Define Histogram according to NCERT solutions class 9 maths chapter 12 ex 12.1?

Answer 2. It is like a bar graph, but it is used to represent continuous class intervals.

Question 3. What do you mean by frequency Polygon?

Answer 3. frequency polygon is a graphic representation of a distribution. Market views are used to understand the form of a distribution.