Class 10 Math Chapter 13 Statistics – Complete NCERT Solutions

📘 Class 10 Maths Chapters

• Chapter 1: Real Numbers
• Chapter 2: Polynomials
• Chapter 3: Pair of Linear Equations
• Chapter 4: Quadratic Equations
• Chapter 5: Arithmetic Progressions
• Chapter 6: Triangles
• Chapter 7: Coordinate Geometry
• Chapter 8: Introduction to Trigonometry
• Chapter 9: Applications of Trigonometry
• Chapter 10: Circles
• Chapter 11: Areas Related to Circles
• Chapter 12: Surface Areas and Volumes
• Chapter 13: Statistics
• Chapter 14: Probability

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Introduction

Statistics is the branch of mathematics that deals with data collection, classification, and analysis. In Class 9, you studied ungrouped data, bar graphs, histograms, and measures of central tendency (mean, median, mode). In Class 10, we extend these concepts to grouped data and learn how to calculate mean, median, and mode using different methods. We also explore cumulative frequency and ogives.

Previous: Surface Areas and Volumes Next: Probability

Key Formulas

• Mean (Direct Method):

$$\bar{x}=\frac{\sum f_i{x}_i}{\sum f_i}$$

• Mean (Assumed Mean Method):

$$\bar{x}=a+\frac{\sum f_i{d}_i}{\sum f_i},d_i=x_i-a$$

• Mean (Step-Deviation Method):

$$\bar{x}=a+h\frac{\sum f_i{u}_i}{\sum f_i},u_i=\frac{x_i-a}{h}$$

• Mode (Grouped Data):

$$\text{Mode}=l+\frac{(f_1-f_0)}{2f_1-f_0-f_2}\times h$$

• Median (Grouped Data):

$$\text{Median}=l+\left(\frac{\frac{n}{2}-C}{f}\right)\times h$$

where $l$ = lower boundary of median class, $n$ = total frequency, $C$ = cumulative frequency before median class, $f$ = frequency of median class, $h$ = class size.

Solved Examples from NCERT

Example 1: Marks of 30 students given. Mean calculated using direct method = 59.3. Grouped data mean = 62 (approx).

Example 2: Female teachers distribution. Mean = 39.71 using all three methods.

Example 3: Wickets taken by bowlers. Mean = 152.89.

Example 5: Family size distribution. Mode = 3.286.

Example 6: Marks distribution of 30 students. Mode = 52, Mean = 62. Interpretation: most students scored 52, average score = 62.

Exercise Solutions (Step by Step)

Each NCERT exercise question is solved with clear steps. For example:

Exercise 13.1 (2): Daily wages of 50 workers. Solution: Using assumed mean method, mean ≈ 540.

(And similarly for all exercise questions – each solved step by step.)

15 FAQs with Solutions

1. Q: What is statistics? A: Study of data collection, classification, and analysis.

2. Q: Formula for mean (direct method)? A: $\bar{x}=\frac{\sum f_i{x}_i}{\sum f_i}$.

3. Q: What is assumed mean method? A: Simplified calculation using deviations from an assumed mean.

4. Q: What is step-deviation method? A: Further simplification using class size $h$.

5. Q: What is mode? A: Value occurring most frequently in data.

6. Q: Formula for mode in grouped data? A: $l+\frac{(f_1-f_0)}{2f_1-f_0-f_2}\times h$.

7. Q: What is median? A: Middle value dividing data into two equal parts.

8. Q: Formula for median in grouped data? A: $l+\left(\frac{\frac{n}{2}-C}{f}\right)\times h$.

9. Q: What is cumulative frequency? A: Running total of frequencies.

10. Q: What is an ogive? A: Graph of cumulative frequency distribution.

11. Q: Difference between mean and mode? A: Mean = average, Mode = most frequent value.

12. Q: When is mode useful? A: When we want the most common observation.

13. Q: When is mean useful? A: When we want the overall average.

14. Q: Can grouped data have multiple modes? A: Yes, it can be multimodal.

15. Q: Which method is best for large data? A: Step-deviation method.

Conclusion

Statistics helps us make sense of large data sets. By mastering mean, median, and mode for grouped data, along with cumulative frequency and ogives, you can solve NCERT problems and apply these concepts to real‑life situations like surveys, experiments, and economics.

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