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The modal class of a distribution turns out to be the very first class of the table. In the mode formula, what should be done about f₀?

Class 10StatisticsStatistics and Probability
  • ATake f₀ equal to f₁, since there is no class before it
  • BTreat the second class as the modal class instead
  • CTake f₀ = 0, since there is no class before the modal class
  • DThe mode cannot be calculated in this situation

Step-by-Step Solution

₀ is the frequency of the class immediately before the modal class. If no such class exists then no observations lie there, so ₀ = 0 and the formula still works, becoming Mode = ₁/₁ − ₂).
Answer: C) Take f₀ = 0, since there is no class before the modal class

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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