Statistical Representation of DataMCQMTP June 22Question 2742 of 295

Relative frequency for a particular class lies between:

Options

\displaystyle 0

and

\displaystyle 1

\displaystyle 0

and

\displaystyle 1

, both inclusive

\displaystyle -1

and

\displaystyle 0

\displaystyle -1

and

\displaystyle 1

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Correct Answer

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

All Options:

A $\displaystyle 0$ and $\displaystyle 1$
B $\displaystyle 0$ and $\displaystyle 1$ , both inclusive
C $\displaystyle -1$ and $\displaystyle 0$
D $\displaystyle -1$ and $\displaystyle 1$

Detailed Solution & Explanation

The relative frequency of a class is defined as the ratio of the frequency of that class (

\displaystyle f_i

) to the total frequency (

\displaystyle N

\displaystyle \sum f_i

) of the distribution:

\text{Relative Frequency} = \frac{f_i}{N}

Since frequency is a count of occurrences, it is always a non-negative number:

f_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:

f_i \le N \implies \frac{f_i}{N} \le 1

Thus, the relative frequency of any class must satisfy the inequality:

0 \le \text{Relative Frequency} \le 1

This means that the relative frequency lies between

\displaystyle 0

and

\displaystyle 1

, **both inclusive** (it can be

\displaystyle 0

if the class contains no observations, or

\displaystyle 1

if all observations fall into that single class). This corresponds to Option B. Hence, **Option B** is the correct answer.

About This Chapter: Statistical Representation of Data

Paper

Paper 3: Quantitative Aptitude

Weightage

2-4 Marks

Key Topics

Data, Frequency Distribution, Graphical Representation

This chapter covers Data, Frequency Distribution, Graphical Representation and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 2-4 Marks weightage. Focus on understanding core concepts rather than memorizing.

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