Correlation and RegressionMCQPYQ Dec 22Question 3677 of 188
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The coefficient of rank correlation between the ranking of following 6 students in two subjects Mathematics and Statistics is: Mathematics | Statistics 3 | 6 5 | 4 8 | 9 4 | 8 7 | 1 10 | 2

Options

A−0.25\displaystyle -0.25
B−0.35\displaystyle -0.35
C0.38\displaystyle 0.38
D−0.20\displaystyle -0.20
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Correct Answer

✅ Option a — −0.25\displaystyle -0.25

All Options:

  • A−0.25\displaystyle -0.25
  • B−0.35\displaystyle -0.35
  • C0.38\displaystyle 0.38
  • D−0.20\displaystyle -0.20

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Detailed Solution & Explanation

**Computing Spearman's Rank Correlation Coefficient:** The data gives marks (not ranks) for 6 students. First, assign ranks: **Mathematics marks:** 3, 5, 8, 4, 7, 10 **Ranking in Maths (ascending):** - 3 → Rank 1, 4 → Rank 2, 5 → Rank 3, 7 → Rank 4, 8 → Rank 5, 10 → Rank 6 **Statistics marks:** 6, 4, 9, 8, 1, 2 **Ranking in Stats (ascending):** - 1 → Rank 1, 2 → Rank 2, 4 → Rank 3, 6 → Rank 4, 8 → Rank 5, 9 → Rank 6 **Rank table:** | Student | Maths Mark | Stats Mark | Rank M (R1\displaystyle R_1) | Rank S (R2\displaystyle R_2) | d=R1−R2\displaystyle d = R_1 - R_2 | d2\displaystyle d^2 | |---|---|---|---|---|---|---| | 1 | 3 | 6 | 1 | 4 | -3 | 9 | | 2 | 5 | 4 | 3 | 3 | 0 | 0 | | 3 | 8 | 9 | 5 | 6 | -1 | 1 | | 4 | 4 | 8 | 2 | 5 | -3 | 9 | | 5 | 7 | 1 | 4 | 1 | 3 | 9 | | 6 | 10 | 2 | 6 | 2 | 4 | 16 | sumd2=9+0+1+9+9+16=44\\sum d^2 = 9 + 0 + 1 + 9 + 9 + 16 = 44 **Formula:** rs=1−frac6sumd2n(n2−1)=1−frac6times446(36−1)=1−frac2646times35=1−frac264210=1−1.257=−0.257approx−0.26r_s = 1 - \\frac{6\\sum d^2}{n(n^2-1)} = 1 - \\frac{6 \\times 44}{6(36-1)} = 1 - \\frac{264}{6 \\times 35} = 1 - \\frac{264}{210} = 1 - 1.257 = -0.257 \\approx -0.26 The closest option is −0.25\displaystyle -0.25. Hence, **Option A** 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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