Statistical Representation of DataMCQPYQ Dec 22Question 2701 of 295
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The suitable formula for computing the number of class intervals is (N\displaystyle N is total frequency)

Options

A3.322log⁡N\displaystyle 3.322 \log N
B0.322log⁡N\displaystyle 0.322 \log N
C1+3.322log⁡N\displaystyle 1 + 3.322 \log N
D1−3.322log⁡N\displaystyle 1 - 3.322 \log N
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Correct Answer

✅ Option c — 1+3.322log⁡N\displaystyle 1 + 3.322 \log N

All Options:

  • A3.322log⁡N\displaystyle 3.322 \log N
  • B0.322log⁡N\displaystyle 0.322 \log N
  • C1+3.322log⁡N\displaystyle 1 + 3.322 \log N
  • D1−3.322log⁡N\displaystyle 1 - 3.322 \log N

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Detailed Solution & Explanation

To determine the optimal number of class intervals (denoted as k\displaystyle k) for a frequency distribution, statisticians often use Sturges' Rule. Herbert Sturges proposed an empirical formula that relates the number of classes to the total number of observations (or total frequency, N\displaystyle N): k=1+3.322log⁡10Nk = 1 + 3.322 \log_{10} N Where: - k\displaystyle k is the number of class intervals (usually rounded to the nearest integer). - log⁡10N\displaystyle \log_{10} N is the base-10 logarithm of the total frequency N\displaystyle N. - 3.322\displaystyle 3.322 is an approximation of 1log⁡102≈3.32193\displaystyle \frac{1}{\log_{10} 2} \approx 3.32193. This formula helps in dividing a continuous dataset into a balanced number of groups to represent the distribution pattern effectively. This corresponds to Option C. Hence, **Option C** 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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