NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3Question 14
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question. 14
14. Given cumulative (less-than) marks of 50 students:
| Marks | Below 20 | Below 40 | Below 60 | Below 80 | Below 100 |
|---|---|---|---|---|---|
| No. of students | 17 | 22 | 29 | 37 | 50 |
Form the ordinary frequency distribution.
Answer:
| Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |
|---|---|---|---|---|---|
| Frequency | 17 | 5 | 7 | 8 | 13 |
Detailed Answer with Explanation:
Step 1: Understand what the given table means.
The numbers given are cumulative frequencies. For example, "Below 40 = 22" means 22 students scored less than 40 marks.
Step 2: Write the class intervals.
The marks are given in groups of 20. So the classes will be: 0–20, 20–40, 40–60, 60–80, 80–100.
Step 3: Find the frequency for each class.
- For 0–20: Directly take "Below 20" = 17.
- For 20–40: Subtract "Below 20" from "Below 40". \(22 - 17 = 5\).
- For 40–60: Subtract "Below 40" from "Below 60". \(29 - 22 = 7\).
- For 60–80: Subtract "Below 60" from "Below 80". \(37 - 29 = 8\).
- For 80–100: Subtract "Below 80" from "Below 100". \(50 - 37 = 13\).
Step 4: Write the ordinary frequency table.
| Class | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |
|---|---|---|---|---|---|
| Frequency | 17 | 5 | 7 | 8 | 13 |
Final Answer: The ordinary frequency distribution is as shown above.