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The class marks of a continuous frequency distribution are 12, 20, 28 and 36. What is the first class interval?

Class 9StatisticsStatistics and Probability
  • A10–14
  • B12–20
  • C8–16
  • D4–12

Step-by-Step Solution

Consecutive class marks differ by 8, so the class size is 8 and half of it is 4. The first class runs from 12 − 4 to 12 + 4, that is 8–16. Treating 12 as a lower limit gives the wrong interval 12–20.
Answer: C) 8–16

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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