Statistical Description of DataMTP June 22Question 2742 of 295
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Relative frequency for a particular class lies between:

Options

A0\displaystyle 0 and 1\displaystyle 1
B0\displaystyle 0 and 1\displaystyle 1, both inclusive
C−1\displaystyle -1 and 0\displaystyle 0
D−1\displaystyle -1 and 1\displaystyle 1
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Correct Answer

✅ Option b — 0\displaystyle 0 and 1\displaystyle 1, both inclusive

All Options:

  • A0\displaystyle 0 and 1\displaystyle 1
  • B0\displaystyle 0 and 1\displaystyle 1, both inclusive
  • C−1\displaystyle -1 and 0\displaystyle 0
  • D−1\displaystyle -1 and 1\displaystyle 1

Detailed Solution & Explanation

The relative frequency of a class is defined as the ratio of the frequency of that class (fi\displaystyle f_i) to the total frequency (N\displaystyle N or ∑fi\displaystyle \sum f_i) of the distribution: Relative Frequency=fiN\text{Relative Frequency} = \frac{f_i}{N} Since frequency is a count of occurrences, it is always a non-negative number: fi≥0  ⟹  fiN≥0f_i \ge 0 \implies \frac{f_i}{N} \ge 0 Additionally, the frequency of any single class cannot exceed the total frequency of all classes: fi≤N  ⟹  fiN≤1f_i \le N \implies \frac{f_i}{N} \le 1 Thus, the relative frequency of any class must satisfy the inequality: 0≤Relative Frequency≤10 \le \text{Relative Frequency} \le 1 This means that the relative frequency lies between 0\displaystyle 0 and 1\displaystyle 1, **both inclusive** (it can be 0\displaystyle 0 if the class contains no observations, or 1\displaystyle 1 if all observations fall into that single class). This corresponds to Option B. Hence, **Option B** is the correct answer.

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