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In a frequency table with the continuous classes 10–20, 20–30 and 30–40, the observation 30 is counted in which class?

Class 9StatisticsStatistics and Probability
  • A20–30
  • B30–40
  • CIn both classes
  • D10–20

Step-by-Step Solution

In continuous (exclusive) form a class holds values from its lower limit up to but not including its upper limit. So 30 is the lower limit of 30–40 and belongs there, never to 20–30, and it is never counted twice.
Answer: B) 30–40

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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