Correlation and RegressionPYQ May 25Question 4392 of 188
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For 9 college students group, the sum of squares of differences in ranks for History and Hindi marks was found to be 62, then what is the value of rank correlation co-efficient?

Options

A1
B0.48
C0.52
D0.87
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Correct Answer

✅ Option b — 0.48

All Options:

  • A1
  • B0.48
  • C0.52
  • D0.87

Detailed Solution & Explanation

Spearman's rank correlation coefficient (R\displaystyle R) is given by the formula:
R=1−6Σd2n(n2−1)R = 1 - \frac{6 \Sigma d^2}{n(n^2 - 1)} Where:
- n=9\displaystyle n = 9 is the number of students.
- Σd2=62\displaystyle \Sigma d^2 = 62 is the sum of squares of differences in ranks.

Let us substitute these values into the formula:
R=1−6×629(92−1)R = 1 - \frac{6 \times 62}{9(9^2 - 1)} R=1−3729(81−1)R = 1 - \frac{372}{9(81 - 1)} R=1−3729×80R = 1 - \frac{372}{9 \times 80} R=1−372720R = 1 - \frac{372}{720} R=1−0.5167=0.4833≈0.48R = 1 - 0.5167 = 0.4833 \approx 0.48
Hence, **Option B** 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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