- A(20, 9)
- B(25, 9)
- C(30, 9)
- D(9, 25)
Step-by-Step Solution
A frequency polygon plots (class mark, frequency). The class mark of 20–30 is , so the point is (25, 9). Using the lower limit 20 is the usual slip.
Answer: B) (25, 9)
A frequency polygon is drawn for the classes 10–20, 20–30 and 30–40 with frequencies 5, 9 and 4. Which point is plotted for the second class?
Class 9StatisticsStatistics and Probability
Key idea: Class intervals and class marks
When data has many distinct values (like heights or weights), group it into **class intervals**.
Example table:
| Class interval | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 4 |
**Class mark** of an interval = (lower limit + upper limit) / 2.
For 0–10: mark = 5. For 10–20: mark = 15.
**Inclusive vs exclusive intervals**:
- Exclusive (continuous) form like 0–10, 10–20: 10 belongs to the SECOND interval, not the first.
- Inclusive form 0–9, 10–19: rare in modern textbooks — convert to continuous form (subtract 0.5 from lower, add 0.5 to upper) before drawing histograms.
Example table:
| Class interval | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 4 |
**Class mark** of an interval = (lower limit + upper limit) / 2.
For 0–10: mark = 5. For 10–20: mark = 15.
**Inclusive vs exclusive intervals**:
- Exclusive (continuous) form like 0–10, 10–20: 10 belongs to the SECOND interval, not the first.
- Inclusive form 0–9, 10–19: rare in modern textbooks — convert to continuous form (subtract 0.5 from lower, add 0.5 to upper) before drawing histograms.
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