Convert the following frequency table into (i) less than form (ii) more than form:
Understand the Problem
The question is asking to convert a given frequency table into two formats: less than form and more than form. The goal is to represent the same data in two different cumulative frequency formats.
Answer
**Less Than Form:** - Less than 10: $3$, - Less than 20: $12$, - Less than 30: $27$, - Less than 40: $57$, - Less than 50: $75$, - Less than 60: $80$ **More Than Form:** - More than 0: $80$, - More than 10: $77$, - More than 20: $68$, - More than 30: $53$, - More than 40: $23$, - More than 50: $5$
Answer for screen readers
Less Than Form:
| Marks | Cumulative Frequency |
|---|---|
| Less than 10 | 3 |
| Less than 20 | 12 |
| Less than 30 | 27 |
| Less than 40 | 57 |
| Less than 50 | 75 |
| Less than 60 | 80 |
More Than Form:
| Marks | Cumulative Frequency |
|---|---|
| More than 0 | 80 |
| More than 10 | 77 |
| More than 20 | 68 |
| More than 30 | 53 |
| More than 40 | 23 |
| More than 50 | 5 |
Steps to Solve
-
Cumulative Frequency Calculation for Less Than Form
We find the cumulative frequency for the less than form by summing the frequencies up to each class interval.
- For 0-10: $3$
- For 10-20: $3 + 9 = 12$
- For 20-30: $12 + 15 = 27$
- For 30-40: $27 + 30 = 57$
- For 40-50: $57 + 18 = 75$
- For 50-60: $75 + 5 = 80$
The less than cumulative frequency table is:
- Less than 10: $3$
- Less than 20: $12$
- Less than 30: $27$
- Less than 40: $57$
- Less than 50: $75$
- Less than 60: $80$
-
Cumulative Frequency Calculation for More Than Form
We find the cumulative frequency for the more than form by summing the frequencies in reverse order, starting from the last group.
- For 50-60: $5$
- For 40-50: $5 + 18 = 23$
- For 30-40: $23 + 30 = 53$
- For 20-30: $53 + 15 = 68$
- For 10-20: $68 + 9 = 77$
- For 0-10: $77 + 3 = 80$
The more than cumulative frequency table is:
- More than 0: $80$
- More than 10: $77$
- More than 20: $68$
- More than 30: $53$
- More than 40: $23$
- More than 50: $5$
Less Than Form:
| Marks | Cumulative Frequency |
|---|---|
| Less than 10 | 3 |
| Less than 20 | 12 |
| Less than 30 | 27 |
| Less than 40 | 57 |
| Less than 50 | 75 |
| Less than 60 | 80 |
More Than Form:
| Marks | Cumulative Frequency |
|---|---|
| More than 0 | 80 |
| More than 10 | 77 |
| More than 20 | 68 |
| More than 30 | 53 |
| More than 40 | 23 |
| More than 50 | 5 |
More Information
The less than form shows how many students scored below each mark range, while the more than form indicates how many students scored above each range.
Tips
- Forgetting to sum the frequencies correctly; double-check your addition.
- Mixing up the less than and more than cumulative frequencies; carefully identify which direction you are summing.
AI-generated content may contain errors. Please verify critical information
