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RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 Statistics

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 Statistics has been provided here. Students can refer to these questions before their examinations for better preparation.
authorImageNeha Tanna18 Nov, 2024
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RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6: This exercise focuses on applying statistical methods to analyze grouped data effectively. Key topics include cumulative frequency distribution, drawing cumulative frequency curves (ogives), and determining measures like the median graphically. Students learn to interpret and solve problems involving data representation through histograms and frequency polygons.

This builds a foundation for data analysis by teaching visualization and interpretation techniques. Step-by-step solutions in RD Sharma emphasize understanding concepts, ensuring students grasp the methodology behind statistical calculations. The exercise is vital for mastering data handling and prepares students for real-world data analysis scenarios.

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 Overview

Exercise 7.6 of RD Sharma Class 10 Maths focuses on Statistics, particularly on calculating the mean, median, and mode for grouped data. These concepts are critical for understanding data representation and analysis in real-life scenarios. Learning these methods equips students with the ability to interpret and summarize large datasets, which is essential for decision-making in fields like economics, business, and research.

This chapter builds a strong foundation for advanced statistical studies in higher classes, enabling students to comprehend and analyze data trends effectively. Practicing these solutions ensures clarity and boosts problem-solving skills.

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 PDF

Below, we have provided the RD Sharma Solutions for Class 10 Maths Chapter 7 Exercise 7.6 (Statistics) in a downloadable PDF format. This comprehensive resource is tailored to help students grasp key statistical concepts, including cumulative frequency distribution, graphical representation, and data interpretation. The step-by-step solutions are crafted to simplify challenging problems, making them accessible and easier to understand. Download the PDF to enhance your preparation, practice effectively, and excel in your Class 10 Maths exams.

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 PDF

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 Statistics

Below is the RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 Statistics -

1. Draw an ogive by less than the method for the following data:

No. of rooms 1 2 3 4 5 6 7 8 9 10
No. of houses 4 9 22 28 24 12 8 6 5 2

Solution:

No. of rooms No. of houses Cumulative Frequency
Less than or equal to 1 4 4
Less than or equal to 2 9 13
Less than or equal to 3 22 35
Less than or equal to 4 28 63
Less than or equal to 5 24 87
Less than or equal to 6 12 99
Less than or equal to 7 8 107
Less than or equal to 8 6 113
Less than or equal to 9 5 118
Less than or equal to 10 2 120
It’s required to plot the points (1, 4), (2, 13), (3, 35), (4, 63), (5, 87), (6, 99), (7, 107), (8, 113), (9, 118), (10, 120), by taking upper-class limit over the x-axis and cumulative frequency over the y-axis. R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 1

2. The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks No. of Students
600 – 640 16
640 – 680 45
680 – 720 156
720 – 760 284
760 – 800 172
800 – 840 59
840 – 880 18

Prepare a cumulative frequency distribution table by less than method and draw an ogive.

Solution:

Marks No. of Students Marks Less than Cumulative Frequency
600 – 640 16 640 16
640 – 680 45 680 61
680 – 720 156 720 217
720 – 760 284 760 501
760 – 800 172 800 673
800 – 840 59 840 732
840 – 880 18 880 750
Plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732), (880, 750) by taking upper class limit over the x-axis and cumulative frequency over the y-axis. R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 2

3. Draw an Ogive to represent the following frequency distribution:

Class-interval 0 – 4 5 – 9 10 – 14 15 – 19 20 – 24
No. of students 2 6 10 5 3

Solution:

Since the given frequency distribution is not continuous, we will have to first make it continuous and then prepare the cumulative frequency:
Class-interval No. of Students Less than Cumulative frequency
0.5 – 4.5 2 4.5 2
4.5 – 9.5 6 9.5 8
9.5 – 14.5 10 14.5 18
14.5 – 19.5 5 19.5 23
19.5 – 24.5 3 24.5 26
Plot the points (4.5, 2), (9.5, 8), (14.5, 18), (19.5, 23), (24.5, 26) by taking the upper-class limit over the x-axis and cumulative frequency over the y-axis. R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 3

4. The monthly profits (in Rs) of 100 shops are distributed as follows:

Profit per shop No of shops:
0 – 50 12
50 – 100 18
100 – 150 27
150 – 200 20
200 – 250 17
250 – 300 6

Draw the frequency polygon for it.

Solution:

Doing for the less than method, we have
Profit per shop Mid-value No of shops:
Less than 0 0 0
Less than 0 – 50 25 12
Less than 50 – 100 75 18
Less than 100 – 150 125 27
Less than 150 – 200 175 20
Less than 200 – 250 225 17
Less than 250 – 300 275 6
Above 300 300 0
By plotting the coordinates respectively, we can get the frequency polygon. R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 4

5. The following distribution gives the daily income of 50 workers of a factory:

Daily income (in Rs): No of workers:
100 – 120 12
120 – 140 14
140 – 160 8
160 – 180 6
180 – 200 10

Convert the above distribution to a ‘less than’ type cumulative frequency distribution and draw its ogive.

Solution:

Firstly, we prepare the cumulative frequency table by less than method as given below:
Daily income Cumulative frequency
Less than 120 12
Less than 140 26
Less than 160 34
Less than 180 40
Less than 200 50
Now we mark on the x-axis upper class limit, y-axis cumulative frequencies. Thus we plot the point (120, 12), (140, 26), (160, 34), (180, 40), (200, 50). R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 5

Benefits of Solving RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6

Solving RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 (Statistics) offers multiple benefits for students. Here are some key advantages:

1. Strengthens Conceptual Understanding

Exercise 7.6 focuses on Statistics, particularly problems related to measures like mean, median, mode, and their applications. By solving these problems, students gain a deep understanding of statistical concepts and their significance in data analysis.

2. Enhances Problem-Solving Skills

RD Sharma's problems are designed to challenge students' problem-solving abilities. Students learn to approach problems step-by-step, which is critical for exams like the CBSE Class 10 Board Exam.

3. Improves Calculation Speed and Accuracy

Statistics problems often require calculations involving large data sets, averages, and frequencies. Regular practice helps improve speed and accuracy in these calculations, reducing errors during exams.

4. Prepares for Board Exams

The exercise includes a variety of questions, from basic to advanced level, aligned with the CBSE syllabus. This comprehensive preparation ensures students are well-prepared for board exam questions based on Statistics.

5. Builds Analytical Thinking

Statistics involves interpreting data, understanding trends, and making logical conclusions. Solving Exercise 7.6 trains students to analyze and interpret data effectively, a skill valuable in academics and real-life applications.

RD Sharma Solutions Class 10 Maths Chapter 7 Exercise 7.6 FAQs

Is RD Sharma enough for maths class 10?

Mathematics for Class 10 R. D. Sharma is the best books for the class 10 CBSE board exam.

Which is the hardest chapter in maths class 10?

The toughest chapter in Class 10 Maths varies among students, but topics like Quadratic Equations, Triangles, and Surface Areas and Volumes are often perceived as challenging due to their abstract concepts and complex calculations.

Is RD Sharma harder than Ncert?

RD Sharma is not tougher than NCERT book.

Is ICSE maths easy?

The most important chapters of ICSE Mathematics include Probability, Statistics, Algebra, Geometry, Trigonometry, Commercial Mathematics and Mensuration. Mathematics is not as easy as it seems. It needs a lot of diligent practice because just a quick practice right before the exam wouldn't help students by any means.
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