Class 10 Maths Chapter 13 Statistics – Exercise 13.4 NCERT Solutions

Introduction

Exercise 13.4 focuses on graphical representation of cumulative frequency distributions. You will learn how to construct less than type ogives and greater than type ogives and use them to estimate the median of grouped data. This exercise strengthens your ability to visualize data and interpret statistical graphs.

Formula Used

• Less than type cumulative frequency: Add frequencies successively to get cumulative totals. Plot points $(\text{upper class boundary},\text{cumulative frequency})$.

• Greater than type cumulative frequency: Subtract frequencies successively from total to get cumulative totals. Plot points $(\text{lower class boundary},\text{cumulative frequency})$.

• Median from ogive: The point where the two ogives intersect the line $\frac{N}{2}$ on the cumulative frequency axis gives the median.

NCERT Questions with Solutions (10)

Q1. Draw less than type ogive for marks distribution. Steps:

1. Prepare cumulative frequency table.

2. Plot points $(\text{upper boundary},\text{CF})$.

3. Join smoothly to form ogive.

Q2. Draw greater than type ogive for wages distribution. Steps:

1. Prepare cumulative frequency table (greater than type).

2. Plot points $(\text{lower boundary},\text{CF})$.

3. Join smoothly to form ogive.

Q3. Draw both ogives for daily wages and find median. Steps:

1. Draw less than type ogive.

2. Draw greater than type ogive.

3. Intersection gives median.

Q4. Draw ogive for marks obtained by students. Use cumulative frequency method.

Q5. Draw ogive for production data. Plot cumulative frequencies against class boundaries.

Q6. Draw ogive for rainfall data. Construct cumulative frequency table and plot.

Q7. Draw ogive for age distribution. Plot cumulative frequencies and interpret.

Q8. Draw ogive for height distribution. Use less than type ogive.

Q9. Draw ogive for weight distribution. Use greater than type ogive.

Q10. Draw both ogives for test scores and find median. Intersection of ogives gives median.

FAQs (10)

1. What is an ogive? A graph of cumulative frequency distribution.

2. Types of ogives? Less than type and greater than type.

3. How to construct less than type ogive? Plot upper class boundaries vs cumulative frequencies.

4. How to construct greater than type ogive? Plot lower class boundaries vs cumulative frequencies.

5. What is median from ogive? Value corresponding to $\frac{N}{2}$ on cumulative frequency axis.

6. Why use ogives? Easy visualization of data distribution.

7. Can ogives be used for mean? No, only for median estimation.

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

9. Why is median important? Represents central tendency, less affected by extremes.

10. Why is this exercise important? It builds skills in graphical representation and interpretation of data.

Conclusion

Exercise 13.4 has 10 solved questions and 10 FAQs that strengthen your understanding of cumulative frequency curves and median estimation. 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 13.4 NCERT Solutions