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The inclusive classes 1–10, 11–20, 21–30 are converted to the exclusive (continuous) form. What is the class mark of the second class after the conversion?

Class 10StatisticsStatistics and Probability
  • A15
  • B15.5
  • C16
  • D10.5

Step-by-Step Solution

The adjustment is (11 − 10)/2 = 0.5, so 11–20 becomes 10.5–20.5. Class mark = (10.5 + 20.5)/2 = 15.5 — the same as (11 + 20)/2, because shifting both limits by the same amount does not move the midpoint.
Answer: B) 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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