ICSE Class 10 Maths Selina Solutions Chapter 23 Graphical Representation (Histograms and Ogives)
In this article we have provided ICSE Class 10 Maths Selina Solutions Chapter 23 prepared by our experts to help students to prepare better for their examinations.
Ananya Gupta25 Jul, 2024
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ICSE Class 10 Maths Selina Solutions Chapter 23: ICSE Class 10 Maths Selina Solutions for Chapter 23 which covers Graphical Representation including Histograms and Ogives provide a detailed guide to understanding these important concepts. Histograms are used to represent frequency distributions of continuous data through bars, while Ogives are cumulative frequency graphs that show how data accumulates over a range of values.
By working through these solutions, students gain valuable skills in data visualization and analysis, important for both exams and practical applications.ICSE Class 10 Maths Selina Solutions Chapter 23 Overview
ICSE Class 10 Maths Selina Solutions for Chapter 23 which focuses on Graphical Representation including Histograms and Ogives are prepared by the subject experts from Physics Wallah. They include detailed, step-by-step instructions and examples to help students understand how to represent and analyze data visually. With this expert guidance, students can gain a clear understanding of these graphical tools, enhancing their ability to interpret data accurately and perform well in their exams.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
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.
Benefits of ICSE Class 10 Maths Selina Solutions Chapter 23
- Enhanced Understanding: The solutions provide clear and detailed explanations of how to construct and interpret histograms and ogives helping students grasp these graphical tools effectively.
- Step-by-Step Guidance: Each solution includes step-by-step instructions making complex concepts more accessible and easier to follow.
- Improved Problem-Solving Skills: The practice problems and solutions help students develop strong problem-solving skills related to data representation, preparing them for exam questions and real-life applications.
- Confidence Building: With thorough explanations and practice students can build confidence in their ability to handle graphical representation problems leading to better performance in exams.
ICSE Class 10 Maths Selina Solutions Chapter 23 FAQs
What is a histogram?
A histogram is a type of bar graph that represents the frequency distribution of continuous data. The data is divided into intervals, and the height of each bar shows the number of data points within that interval.
How do you construct a histogram?
To construct a histogram, first create intervals (bins) for the data. Then, plot bars where the width of each bar corresponds to an interval and the height represents the frequency of data points in that interval. Ensure the bars touch each other to indicate continuous data.
What is an ogive?
An ogive is a cumulative frequency graph that shows how data accumulates over a range of values. It helps in understanding the distribution of data by plotting cumulative frequencies against the upper boundaries of intervals.
How do you construct an ogive?
To construct an ogive, plot cumulative frequencies on the y-axis against the upper boundaries of intervals on the x-axis. Connect the points with a smooth curve to represent the cumulative frequency distribution.
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