Correlation and RegressionPYQ Sept 25Question 4494 of 188
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The sum of squares of the differences between two ranks awarded by two judges on 10 candidates is _______ if the rank correlation coefficient is 0.8.

Options

A44
B55
C66
D33
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Correct Answer

✅ Option d — 33

All Options:

  • A44
  • B55
  • C66
  • D33

Detailed Solution & Explanation

Let us calculate the sum of squares of differences in ranks (∑d2\displaystyle \sum d^2) using Spearman's rank correlation coefficient formula:
1. **Given Data**:
- Number of candidates: n=10\displaystyle n = 10
- Rank correlation coefficient: rk=0.8\displaystyle r_k = 0.8
2. **Formula for Spearman's Rank Correlation Coefficient**:
rk=1−6∑d2n(n2−1)r_k = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}
3. **Calculation**:
Substitute the given values into the formula:
0.8=1−6∑d210(102−1)0.8 = 1 - \frac{6 \sum d^2}{10(10^2 - 1)}
0.8=1−6∑d210(99)0.8 = 1 - \frac{6 \sum d^2}{10(99)}
0.8=1−6∑d29900.8 = 1 - \frac{6 \sum d^2}{990}
Rearranging the terms to solve for ∑d2\displaystyle \sum d^2:
6∑d2990=1−0.8=0.2\frac{6 \sum d^2}{990} = 1 - 0.8 = 0.2
6∑d2=0.2×990=1986 \sum d^2 = 0.2 \times 990 = 198
∑d2=1986=33\sum d^2 = \frac{198}{6} = 33
Therefore, the sum of squares of the differences in ranks is 33\displaystyle 33.
Hence, **Option D** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

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