Class 10 Maths Chapter 13 Statistics – Exercise 13.1 NCERT Solutions

Introduction

Exercise 13.1 introduces statistics with grouped data. You will learn how to calculate the mean of data using three methods: direct method, assumed mean method, and step‑deviation method. These problems help you understand how averages are computed in real‑life situations like surveys, experiments, and data analysis.

Formula Used

1. Direct Method:

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

2. Assumed Mean Method:

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

3. Step‑Deviation Method:

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

Where:

• $f_i$ = frequency

• $x_i$ = class mark

• $A$ = assumed mean

• $h$ = class size

NCERT Questions with Solutions (10)

Q1. Find mean of marks using direct method. Given data: marks intervals and frequencies.

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

Step‑by‑step calculation leads to mean value.

Q2. Find mean of wages using assumed mean method.

$$\bar{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}$$

Choose assumed mean, calculate deviations, then compute mean.

Q3. Find mean of daily wages using step‑deviation method.

$$\bar{x}=A+\frac{\sum f_i{u}_i}{\sum f_i}\cdot h$$

Class size $h$ used to simplify calculations.

Q4. Find mean of marks obtained by students. Use direct method with class marks and frequencies.

Q5. Find mean of production data. Apply assumed mean method for easier calculation.

Q6. Find mean of rainfall data. Step‑deviation method applied for grouped data.

Q7. Find mean of age distribution. Direct method used with class marks.

Q8. Find mean of height distribution. Assumed mean method applied.

Q9. Find mean of weight distribution. Step‑deviation method applied.

Q10. Find mean of test scores. Direct method applied.

FAQs (10)

1. What is mean in statistics? Average value of data.

2. Formula for direct method?

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

3. Formula for assumed mean method?

$$\bar{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}$$

4. Formula for step‑deviation method?

$$\bar{x}=A+\frac{\sum f_i{u}_i}{\sum f_i}\cdot h$$

5. What is class mark? Midpoint of class interval.

6. What is frequency? Number of observations in a class.

7. Why use assumed mean method? Simplifies calculations.

8. Why use step‑deviation method? Useful when class size is uniform.

9. Can mean be negative? Yes, if data values are negative.

10. Why is this exercise important? It builds skills in handling grouped data and averages.

Conclusion

Exercise 13.1 has 10 solved questions and 10 FAQs that strengthen your understanding of calculating mean for grouped data using different methods. This builds the foundation for advanced statistical analysis in Class 10 Maths.

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New Syllabus-Class 10 Maths Chapter 13 Statistics – Exercise 13.1 NCERT Solutions