Class 10 Maths Chapter 13 Statistics – Exercise 13.2 NCERT Solutions

Introduction

Exercise 13.2 focuses on finding the median of grouped data. The median is the middle value of a dataset when arranged in ascending order. For grouped frequency distributions, we use a formula involving the median class, cumulative frequency, and class size. This exercise strengthens your ability to analyze data distributions.

Formula Used

For a grouped frequency distribution:

$$\text{Median}=L+\left(\frac{\frac{N}{2}-CF}{f}\right)\cdot h$$

Where:

• $L$ = lower boundary of median class

• $N$ = total frequency ($\sum f_i$)

• $CF$ = cumulative frequency before median class

• $f$ = frequency of median class

• $h$ = class size

NCERT Questions with Solutions (10)

Q1. Find median of marks distribution given in frequency table. Steps:

1. Compute cumulative frequencies.

2. Identify median class where cumulative frequency $\ge \frac{N}{2}$.

3. Apply formula.

$$\text{Median}=L+\left(\frac{\frac{N}{2}-CF}{f}\right)\cdot h$$

Q2. Find median of wages distribution. Follow same steps: cumulative frequency, median class, apply formula.

Q3. Find median of daily wages of workers.

$$\text{Median}=L+\left(\frac{\frac{N}{2}-CF}{f}\right)\cdot h$$

Q4. Find median of marks obtained by students. Identify median class and compute.

Q5. Find median of production data. Use cumulative frequency method.

Q6. Find median of rainfall data. Apply formula with median class.

Q7. Find median of age distribution. Compute cumulative frequencies, locate median class.

Q8. Find median of height distribution. Apply formula step by step.

Q9. Find median of weight distribution. Use grouped data formula.

Q10. Find median of test scores.

$$\text{Median}=L+\left(\frac{\frac{N}{2}-CF}{f}\right)\cdot h$$

FAQs (10)

1. What is median? Middle value of dataset.

2. Formula for median of grouped data?

$$\text{Median}=L+\left(\frac{\frac{N}{2}-CF}{f}\right)\cdot h$$

3. What is median class? Class interval containing the middle value.

4. What is cumulative frequency? Running total of frequencies.

5. Why use median? It is less affected by extreme values.

6. Difference between mean and median? Mean = average, Median = middle value.

7. Can median be negative? Yes, if dataset has negative values.

8. Is median always unique? Yes, for a given dataset.

9. Why is median important? Used in surveys, economics, and social sciences.

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

Conclusion

Exercise 13.2 has 10 solved questions and 10 FAQs that strengthen your understanding of calculating median for grouped data. This builds the foundation for advanced statistical analysis in Class 10 Maths.

Visit: www.fuzymathacademy.com

New Syllabus-Class 10 Maths Chapter 13 Statistics – Exercise 13.2 NCERT Solutions