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By Karan Singh Bisht
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Updated on 11 Jun 2025, 18:11 IST
RD Sharma Solutions for Class 10 Maths Chapter 7 – Statistics are available for easy access, making it a perfect resource for last-minute revisions. Whether you're looking to brush up on key concepts or formulas, RD Sharma Solutions serve as a reliable guide to help you prepare for exams and score high. Created by our team of experts at Infinity Learn, these solutions are designed in simple language with clear explanations, aligned with the latest CBSE guidelines.
RD Sharma Class 10 Solutions for Chapter 7, Statistics, is one of the most interesting chapters, comprising six exercises. The chapter focuses on techniques for calculating the mean, median, and mode of grouped data.
It also introduces the concept of the cumulative frequency graph for a frequency distribution. Students can access solutions for all exercises in this chapter through RD Sharma Solutions for Class 10.
RD Sharma Class 10 Chapter 7 PDF includes detailed solutions, examples, and extra questions to help you master Statistics and other topics. Click here to download the RD Sharma Class 10 Chapter 7 PDF.
Question 1: Find the mean of the following data:
Class intervals: 0-10, 10-20, 20-30, 30-40, 40-50
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Frequencies: 5, 8, 10, 7, 3
Solution: Midpoints: 5, 15, 25, 35, 45
Products: 5 x 5 = 25, 15 x 8 = 120, 25 x 10 = 250, 35 x 7 = 245, 45 x 3 = 135
Sum of products: 25 + 120 + 250 + 245 + 135 = 775
Sum of frequencies: 5 + 8 + 10 + 7 + 3 = 33
Mean = 775 / 33
= 23.48
Question 2: Find the median of the following data:
Class intervals: 10-20, 20-30, 30-40, 40-50
Frequencies: 3, 6, 9, 2
Solution:
Cumulative frequency: 3, 9, 18, 20
Median class: 30-40
Median = L + ((N/2 - CF) / f) × h
Median = 30 + ((10 - 9) / 9) × 10
= 30 + 7.14
= 31.11
Question 3: Find the mode of the following data:
Class intervals: 0-10, 10-20, 20-30, 30-40, 40-50
Frequencies: 6, 10, 12, 8, 4
Solution:
Modal class: 20-30
Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) × h
Mode = 20 + ((12 - 10) / (2(12) - 10 - 8)) × 10
= 20 + 3.33
= 23.33
Question 4: Find the cumulative frequency distribution for the following data:
Class intervals: 0-5, 5-10, 10-15, 15-20
Frequencies: 2, 3, 5, 4
Solution:
Cumulative frequencies: 2, 5, 10, 14
Question 5: For the following data, find the mean:
Class intervals: 1-5, 6-10, 11-15, 16-20
Frequencies: 3, 7, 5, 2
Solution:
Midpoints: 3, 8, 13, 18
Products: 3 x 3 = 9, 8 x 7 = 56, 13 x 5 = 65, 18 x 2 = 36
Sum of products: 9 + 56 + 65 + 36 = 166
Sum of frequencies: 3 + 7 + 5 + 2 = 17
Mean = 166 / 17
= 9.76
Question 6: Find the median from the following cumulative frequency distribution:
Class intervals: 0-10, 10-20, 20-30, 30-40
Cumulative frequencies: 5, 12, 18, 20
Solution:
Median class: 10-20
Median = L + ((N/2 - CF) / f) × h
Median = 10 + ((10 - 9) / 7) × 10
= 10 + 7.14
= 17.14
Question 7: Find the mode from the following data:
Class intervals: 5-10, 10-15, 15-20, 20-25
Frequencies: 3, 8, 12, 7
Solution:
Modal class: 15-20
Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) × h
Mode = 15 + ((12 - 8) / (2(12) - 8 - 7)) × 5
= 15 + 2.22
= 17.22
Question 8: Find the mean of the following frequency distribution:
Class intervals: 10-20, 20-30, 30-40
Frequencies: 6, 4, 5
Solution:
Midpoints: 15, 25, 35
Products: 15 x 6 = 90, 25 x 4 = 100, 35 x 5 = 175
Sum of products: 90 + 100 + 175 = 365
Sum of frequencies: 6 + 4 + 5 = 15
Mean = 365 / 15
= 24.33
Question 9: Calculate the mean for the following data:
Class intervals: 5-10, 10-15, 15-20
Frequencies: 2, 3, 5
Solution:
Midpoints: 7.5, 12.5, 17.5
Products: 7.5 x 2 = 15, 12.5 x 3 = 37.5, 17.5 x 5 = 87.5
Sum of products: 15 + 37.5 + 87.5 = 140
Sum of frequencies: 2 + 3 + 5 = 10
Mean = 140 / 10
= 14
Question 10: Find the median from the following cumulative frequency table:
Class intervals: 10-20, 20-30, 30-40, 40-50
Cumulative frequencies: 4, 9, 14, 20
Solution:
Median class: 20-30
Median = L + ((N/2 - CF) / f) × h
Median = 20 + ((10 - 9) / 5) × 10
= 20 + 12
= 32
RD Sharma Solutions provide detailed and step-by-step explanations of statistical concepts such as mean, median, mode, and cumulative frequency graphs. Practicing these solutions enhances problem-solving skills and builds confidence, which is essential for performing well in board exams.
This chapter focuses on techniques for calculating the mean, median, and mode of grouped data. It also introduces the concept of cumulative frequency graphs, which are essential for data analysis.
Yes, practicing all exercises is recommended as they encompass a variety of problems that can appear in exams. This comprehensive practice helps in understanding different problem-solving approaches and boosts confidence.
Sir Francis Galton is often referred to as the father of statistics. He made significant contributions to the field, including the development of regression and correlation concepts.
These solutions offer a structured approach to understanding statistical concepts, provide ample practice problems, and enhance analytical skills. Regular practice with these solutions can lead to a better grasp of the subject and improved exam performance.