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Assertion (A): The class mark of the interval 20–30 is 20. Reason (R): The class mark is the midpoint of a class interval. Which is correct?

Class 9StatisticsStatistics and Probability
  • ABoth A and R are true and R correctly explains A
  • BBoth A and R are true but R does not explain A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

The class mark of 20–30 is , not 20 — 20 is only the lower limit, so A is false. R states the correct definition, so R is true.
Answer: D) A is false but R is true

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.

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