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For that same "less than" table (less than 10: 5, less than 20: 14, less than 30: 30, less than 40: 42, less than 50: 50), which class is the modal class?

Class 10StatisticsStatistics and Probability
  • A20–30
  • B40–50
  • C30–40
  • D0–10

Step-by-Step Solution

Convert to class frequencies first: 5, 9, 16, 12, 8. The largest is 16, so the modal class is 20–30. Reading the cumulative column directly would wrongly point to 40–50, because cumulative frequencies always keep growing.
Answer: A) 20–30

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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