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A distribution is written in inclusive form as 10–19, 20–29, 30–39, 40–49. The true class limits (class boundaries) of the class 20–29 are ____.

Class 10StatisticsStatistics and Probability
  • A20.5–29.5
  • B19.5–28.5
  • C19.5–29.5
  • D20–30

Step-by-Step Solution

The gap between 19 and 20 is 1, so the adjustment is 1/2 = 0.5. Subtract 0.5 from the lower limit and add 0.5 to the upper limit: 20 − 0.5 = 19.5 and 29 + 0.5 = 29.5, giving 19.5–29.5.
Answer: C) 19.5–29.5

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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