R.D. Sharma Solutions Class10 Mathematics

Why R.D. Sharma Solutions Are Important

R.D. Sharmas textbooks have been the backbone of Indian school mathematics for decades. The solutions provided with each exercise make the difference between surfacelevel learning and a firm conceptual grasp. For Class10, where the CBSE board exams emphasize problemsolving ability, the solutions are designed to:

• Illustrate stepbystep reasoning, not just the final answer.
• Highlight common pitfalls that students often overlook.
• Bridge the gap between theory and application, especially in dataintensive topics like Statistics.

The solutions are aligned with the latest CBSE syllabus, ensuring that every method matches the examinations expectations.

Chapter7 Statistics: A Quick Recap

Statistics in Class10 focuses on handling data sets, calculating measures of central tendency, and understanding dispersion. The main objectives are to:

• Interpret grouped data presented in frequency tables.
• Compute mean, median, and mode for both ungrouped and grouped data.
• Determine range and understand its significance.
• Apply the concept of class intervals in realworld contexts.

Exercise7.1 is the first set of practice questions after theory. It includes:

• Basic calculations of mean, median, and mode for small data sets.
• Questions that require drawing conclusions from given data.
• Problems that test the ability to spot errors in data entries.

Exercise7.1 What to Expect

The 7.1 exercise contains ten questions (110) that progressively increase in difficulty. A typical question may present a table of marks scored by a class of students or the number of items sold per day, asking the learner to compute the required statistical parameter.

For example, Question3 may read:

The solutions for each question follow a consistent format:

1. Restate the question in a concise form.
2. List relevant data points clearly.
3. Show each step of calculation with proper formulae.
4. Present the final answer and, where required, a brief interpretation.

Detailed Solutions for Exercise7.1

Question1

Problem: Find the mean of the numbers 12, 15, 20, 25, 28.

Solution:

1. Sum the numbers: 12 + 15 + 20 + 25 + 28 = 100.
2. Count of numbers = 5.
3. Mean = Total / Count = 100 5 = 20.

Question2

Problem: The following data represent the ages (in years) of a group of 8 children: 6, 7, 7, 8, 9, 9, 10, 12. Find the median.

Solution:

1. Arrange data in ascending order (already arranged).
2. Number of observations = 8 (even).
3. Middle positions = 4th and 5th values 8 and 9.
4. Median = (8 + 9) / 2 = 8.5 years.

Question3 (example shown earlier)

Solution:

1. Mode: The value occurring most frequently is 55 (appears three times). Mode = 55.
2. Median:
   • Number of observations = 12 (even).
   • Middle positions = 6th & 7th values 55 and 55.
   • Median = (55 + 55) / 2 = 55.
3. Mean:
   • Sum = 40+45+45+50+55+55+55+60+65+70+70+75 = 645.
   • Mean = 645 12 = 53.75.

Question4

Problem: In a class of 30 students, the number of books read in a month is shown:
02books: 5 students35books: 12 students68books: 9 students911books: 4 students. Find the mean number of books read (use classmidpoint method).

Solution:

1. Find midpoints of each class:
   • 02 1
   • 35 4
   • 68 7
   • 911 10
2. Multiply each midpoint by its frequency and add:
   • 1 5 = 5
   • 4 12 = 48
   • 7 9 = 63
   • 10 4 = 40
   Total = 5 + 48 + 63 + 40 = 156.
3. Total number of students = 30.
4. Mean = 156 30 = 5.2 books.

Question5

Problem: A set of numbers is 3, 5, 7, 9, 11. Show that the mean, median and mode are in an arithmetic progression.

Solution:

1. Mean = (3+5+7+9+11) / 5 = 35 5 = 7.
2. Median (middle value) = 7.
3. Since no number repeats, there is no mode. In this context, the mode is considered not defined, therefore the three terms cannot form an AP. The question tests understanding that a mode must exist; hence the statement is false.

Question6 10

Solutions for the remaining questions follow the same structured approach: list data, use appropriate formulae, compute, and provide a concise interpretation. The key points covered in these solutions include:

• Identifying whether data is grouped or ungrouped.
• Choosing the correct classmidpoint for grouped data.
• Using the formula Mean = fx / f where f is frequency and x is midpoint.
• Checking for multiple modes (bimodal or multimodal sets).
• Understanding the impact of outliers on the mean and median.

Full stepbystep solutions for questions6to10 can be accessed in the downloadable PDF linked below, providing ample practice for the CBSE board exam.

Download Complete Solution PDF

Study Tips for Mastering Statistics

• Memorise formulas: Mean, median, mode, and range formulas should be at your fingertips.
• Practice classmidpoint calculations: Many errors arise from using incorrect midpoints.
• Check work by reverse calculation: After finding a mean, multiply it by the total frequency to ensure you retrieve the original sum.
• Use a systematic layout: Write data in tables; this reduces arithmetic mistakes.
• Interpret results: In exam questions, after computing the statistic, comment on the datas nature (e.g., high median indicates overall good performance).

Wrapping Up

R.D. Sharmas solutions for Exercise7.1 offer a clear pathway from raw data to meaningful statistical insights. By following the stepbystep approach, students not only learn how to compute mean, median, and mode but also develop the ability to analyse data criticallyan essential skill for the CBSE Class10 Mathematics examination and beyond.

Consistent practice with these solutions, combined with the study tips above, will build confidence and ensure that the concepts of Statistics become second nature. Keep revisiting the solved examples whenever a new problem appears, and soon the entire chapter will feel intuitive.