Correlation and RegressionMCQMTP June 22Question 3684 of 188
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In a bivariate distribution if the rank correlation coefficient r=0.12\displaystyle r = 0.12, Sigmad2=146\displaystyle \\Sigma d^2 = 146. Then the no. of observed pairs (N)\displaystyle (N) is

Options

A9\displaystyle 9
B8\displaystyle 8
C7\displaystyle 7
D10\displaystyle 10
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Correct Answer

✅ Option d — 10\displaystyle 10

All Options:

  • A9\displaystyle 9
  • B8\displaystyle 8
  • C7\displaystyle 7
  • D10\displaystyle 10

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Detailed Solution & Explanation

**Finding number of pairs from Spearman's formula:** Given: - rs=0.12\displaystyle r_s = 0.12 - sumd2=146\displaystyle \\sum d^2 = 146 **Formula:** rs=1−frac6sumd2n(n2−1)r_s = 1 - \\frac{6\\sum d^2}{n(n^2-1)} 0.12=1−frac6times146n(n2−1)0.12 = 1 - \\frac{6 \\times 146}{n(n^2-1)} frac876n(n2−1)=1−0.12=0.88\\frac{876}{n(n^2-1)} = 1 - 0.12 = 0.88 n(n2−1)=frac8760.88=995.45...n(n^2-1) = \\frac{876}{0.88} = 995.45... Let's try n=10\displaystyle n = 10: n(n2−1)=10(100−1)=10times99=990n(n^2-1) = 10(100-1) = 10 \\times 99 = 990 Check: rs=1−frac6times146990=1−frac876990=1−0.8848...=0.115approx0.12\displaystyle r_s = 1 - \\frac{6 \\times 146}{990} = 1 - \\frac{876}{990} = 1 - 0.8848... = 0.115 \\approx 0.12 ✓ So N=10\displaystyle N = 10. 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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