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The inclusive table reads 1–5: 3, 6–10: 9, 11–15: 15, 16–20: 12, 21–25: 6. Written in exclusive (continuous) form, the modal class is ____.

Class 10StatisticsStatistics and Probability
  • A10.5–15.5
  • B11–15
  • C15.5–20.5
  • D10.5–14.5

Step-by-Step Solution

The highest frequency is 15, so the modal class is 11–15. The gap between 5 and 6 is 1, so subtract and add 0.5: in continuous form it is 10.5–15.5. The mode formula must use these boundaries, otherwise l is wrong by 0.5.
Answer: A) 10.5–15.5

Key idea: Mode for grouped data

**Modal class**: class with HIGHEST frequency.

**Mode formula**:
**Mode = ₁ − ₀) / ₁ − ₀ − ₂)**

Where:
- = lower limit of modal class
- = class width
- ₁ = frequency of modal class
- ₀ = frequency of class BEFORE modal class
- ₂ = frequency of class AFTER modal class

**Example**: Modal class 30–40 with ₁ = 12, ₀ = 5, ₂ = 8. .
Mode = ≈ 36.36.

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