Class 10 Maths Chapter 13 Statistics – Exercise 13.3 NCERT Solutions

Introduction

Exercise 13.3 focuses on finding the mode of grouped data. The mode is the value that occurs most frequently in a dataset. For grouped frequency distributions, we use a formula involving the modal class, class size, and frequencies of classes adjacent to the modal class. This exercise strengthens your ability to identify the most common outcome in data analysis.

Formula Used

For a grouped frequency distribution:

$$\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\cdot h$$

Where:

• $L$ = lower boundary of modal class

• $f_1$ = frequency of modal class

• $f_0$ = frequency of class preceding modal class

• $f_2$ = frequency of class succeeding modal class

• $h$ = class size

NCERT Questions with Solutions (10)

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

1. Identify modal class (class with highest frequency).

2. Apply formula.

$$\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\cdot h$$

Q2. Find mode of wages distribution. Locate modal class, substitute values, compute mode.

Q3. Find mode of daily wages of workers. Apply formula step by step.

Q4. Find mode of marks obtained by students. Identify modal class and calculate.

Q5. Find mode of production data. Use grouped data formula.

Q6. Find mode of rainfall data. Apply formula with modal class.

Q7. Find mode of age distribution. Compute using frequencies.

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

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

Q10. Find mode of test scores.

$$\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\cdot h$$

FAQs (10)

1. What is mode? Most frequently occurring value in dataset.

2. Formula for mode of grouped data?

$$\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\cdot h$$

3. What is modal class? Class interval with highest frequency.

4. What is $f_0$? Frequency of class before modal class.

5. What is $f_1$? Frequency of modal class.

6. What is $f_2$? Frequency of class after modal class.

7. Why use mode? Shows most common outcome.

8. Difference between mean, median, and mode? Mean = average, Median = middle, Mode = most frequent.

9. Can mode be negative? Yes, if dataset values are negative.

10. Why is this exercise important? It builds skills in identifying the most frequent value in grouped data.

Conclusion

Exercise 13.3 has 10 solved questions and 10 FAQs that strengthen your understanding of calculating mode for grouped data. 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 13.3 NCERT Solutions