ICSE Class 10 Maths Selina Solutions Chapter 23 Graphical Representation (Histograms and Ogives)
Ananya Gupta17 Feb, 2026
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ICSE Class 10 Board Exams have started from today, 17 February 2026, revising important chapters is crucial for scoring well. ICSE Class 10 Maths Selina Solutions Chapter 23 provides clear explanations, step-by-step methods, and practice problems to help students strengthen their understanding of key concepts.
These solutions make last-minute revision easier and help students approach the upcoming Mathematics exam confidently.
ICSE Class 10 Maths Selina Solutions Chapter 23 Graphical Representation (Histograms and Ogives)
Below we have provided the ICSE Class 10 Maths Selina Solutions for Chapter 23 on Graphical Representation (Histograms and Ogives) to assist students. These solutions provide detailed explanations and step-by-step guidance on how to construct and interpret histograms and ogives, helping students master these important data representation techniques.ICSE Class 10 Maths Selina Solutions Chapter 23 Exercise 23 A Page No: 348
1. Draw histograms for the following frequency distributions:
(i)
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Frequency | 12 | 20 | 26 | 18 | 10 | 6 |
(ii)
| Class Interval | 10-16 | 16-22 | 22-28 | 28-34 | 34-40 |
| Frequency | 15 | 23 | 30 | 20 | 16 |
(iii)
| Class Interval | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 |
| Frequency | 24 | 16 | 09 | 15 | 20 |
(iv)
| Class Marks | 16 | 24 | 32 | 40 | 48 | 56 | 64 |
| Frequency | 8 | 12 | 15 | 18 | 25 | 19 | 10 |
Solution:
(i)| Class Interval | Frequency |
| 0-10 | 12 |
| 10-20 | 20 |
| 20-30 | 26 |
| 30-40 | 18 |
| 40-50 | 10 |
| 50-60 | 06 |
Steps of construction: (a) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis. (b) Construct rectangles with class intervals as bases and corresponding frequencies as heights. (ii)
| Class Interval | Frequency |
| 10-16 | 15 |
| 16-22 | 23 |
| 22-28 | 30 |
| 28-34 | 20 |
| 34-40 | 16 |
Steps of construction: (a) Taking suitable scales, mark the class intervals on x-axis and frequency on y-axis. (b) Construct rectangles with class intervals as bases and corresponding frequencies as heights. (iii)
| Class Interval (Inclusive form) | Class Interval (Exclusive Form) | Frequency |
| 30-39 | 29.5-39.5 | 24 |
| 40-49 | 39.5-49.5 | 16 |
| 50-59 | 49.5-59.5 | 09 |
| 60-69 | 59.5-69.5 | 15 |
| 70-79 | 69.5-79.5 | 20 |
Steps of construction: (a) Convert the data into exclusive form. [Here, adjustment factor = 0.5] (b) Taking suitable scales, mark the class intervals on x-axis and the frequency on y-axis. (c) Construct rectangles with class intervals as bases and corresponding frequencies as heights. (iv) From the given data:
| Class Marks | Class Intervals | Frequency |
| 16 | 12-20 | 08 |
| 24 | 20-28 | 12 |
| 32 | 28-36 | 15 |
| 40 | 36-44 | 18 |
| 48 | 44-52 | 25 |
| 56 | 52-60 | 19 |
| 64 | 60-68 | 10 |
Steps of construction: (a) Convert the class marks into class intervals. (b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis. (c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.
2. Draw cumulative frequency curve (ogive) for each of the following distributions:
(i)
| Class
Interval |
10-15 | 15-20 | 20-25 | 25-30 | 30-45 | 35-40 |
| Frequency | 10 | 15 | 17 | 12 | 10 | 08 |
(ii)
| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
| Frequency | 23 | 16 | 15 | 20 | 12 |
Solution:
(i)| Class Interval | Frequency |
| 10-15 | 10 |
| 15-20 | 15 |
| 20-25 | 17 |
| 25-30 | 12 |
| 30-35 | 10 |
| 35-40 | 08 |
Steps of construction: (a) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis. (b) Construct rectangles with class intervals as bases and corresponding frequencies as heights. (c) Join the mid-points of the rectangle to obtain the ogive. (ii)
| Class Interval (Inclusive) | Class Interval (Exclusive) | Frequency | Cumulative Frequency |
| 10-19 | 9.5-19.5 | 23 | 23 |
| 20-29 | 19.5-29.5 | 16 | 39 |
| 30-39 | 29.5-39.5 | 15 | 54 |
| 40-49 | 39.5-49.5 | 20 | 74 |
| 50-59 | 49.5-59.5 | 12 | 86 |
| Total | 86 |
Steps of construction: (a) Convert the data into exclusive form. [Here, adjustment factor = 0.5] (b) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis. (c) Construct rectangles with class intervals as bases and corresponding frequencies as heights. (d) Join the mid-points of the rectangle to obtain the ogive.
3. Draw an ogive for each of the following distributions:
(i)
| Marks Obtained | less
than 10 |
less
than 20 |
less
than30 |
less
than 40 |
less
than 50 |
| No. of
Students |
8 | 25 | 38 | 50 | 67 |
(ii)
| Age in years (less than) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| Cumulative Frequency | 0 | 17 | 32 | 37 | 53 | 58 | 65 |
Solution:
(i)| Marks Obtained | No. of students (c.f.) |
| less than 10 | 8 |
| less than 20 | 25 |
| less than 30 | 38 |
| less than 40 | 50 |
| less than 50 | 67 |
Steps Of construction: (a) Plot the points (10, 8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph. (b) Join them with free hand to obtain an ogive. (ii)
| Age in years (less than) | Cumulative Frequency |
| 10 | 0 |
| 20 | 17 |
| 30 | 32 |
| 40 | 37 |
| 50 | 53 |
| 60 | 58 |
| 70 | 65 |
Steps Of construction: (a) Plot the points (10, 0), (20, 17), (30, 32), (40, 37), (50, 53), (60, 58) and (70, 65) on the graph. (b) Join them with free hand to obtain an ogive.
4. Construct a frequency distribution table for the number given below, using the class intervals 21-30, 31-40 … etc.
75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36, 47
Use the table obtained to draw:
(i) a histogram (ii) an ogive
Solution:
(i) 
(ii) 
Plot the points (30,4), (40,13), (50,22), (60,29), (70,37) and (80,40) on the graph and join them with free hand to obtain an ogive.
ICSE Class 10 Maths Selina Solutions Chapter 23 PDF
The PDF link for ICSE Class 10 Maths Selina Solutions Chapter 23 which covers Graphical Representation including Histograms and Ogives, is available below. Students are advised to prepare using the ICSE Class 10 Maths Selina Solutions for Chapter 23 before the examinations to improve their performance.
ICSE Class 10 Maths Selina Solutions Chapter 23 PDF.
Last Days Preparation Strategy for Chapter 23 – ICSE Class 10 Maths
As the ICSE Class 10 Board Exams have started from 17 February 2026 and the Mathematics exam is scheduled for 2 March 2026, revising Chapter 23 Selina Solutions effectively in the last few days can boost confidence and help secure high marks. Here’s a focused strategy:
Revise Important Topics
Focus on all the key concepts and problem types in Chapter 23, including formulas, examples, and frequently asked questions. Prioritize high-weightage topics to ensure maximum scoring potential in the board exam.
Make Quick Notes
Create concise notes or flashcards of important formulas, theorems, and step-by-step methods for solving different types of problems. These will help in fast last-minute revision and quick recall during the exam.
Practice Problem Sets
Solve previous years’ questions, sample papers, and exercise problems from the chapter. Pay special attention to recurring question patterns and tricky sums to improve speed and accuracy.
Understand Concepts Clearly
Instead of memorizing steps blindly, focus on understanding the underlying concepts and logic behind each type of problem. Concept clarity ensures you can solve application-based and higher-order questions confidently.
ICSE Class 10 Maths Selina Solutions Chapter 23 FAQs
What is a histogram?
How do you construct a histogram?
What is an ogive?
How do you construct an ogive?
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