Spearman's rank correlation coefficient rs is given by

Option a: 1 - 6 d2/n(n2 - 1). Solution: Spearman's Rank Correlation Coefficient Formula: Spearman's rank correlation coefficient is: rs = 1 - 6 di2/n(n2-1) where: - di = R1i - R2i = difference in ranks of the i -th pair - n = number of pairs of observations Verification of other options: - Option (b): Uses + sign — incorrect, gives values > 1 when d2 > 0 - Option (c): Missing n in denominator — incorrect - Option (d): Uses n(n2+1) — incorrect denominator The correct formula is Option (a): rs = 1 - 6 d2/n(n2-1) Note: The given correctoption says 'd', but Option A is the standard and correct Spearman's formula. Hence, Option A is the correct answer.

Spearman's rank correlation coefficient $r_s$ is given by

The correct answer is Option a: $1 - \\frac{6 \\sum d^2}{n(n^2 - 1)}$. **Spearman's Rank Correlation Coefficient Formula:** Spearman's rank correlation coefficient is: $$r_s = 1 - \\frac{6\\sum d_i^2}{n(n^2-1)}$$ where: - $d_i = R_{1i} - R_{2i}$ = difference in ranks of the $i$-th pair - $n$ = number of pairs of observations **Verification of other options:** - Option (b): Uses $+$ sign — incorrect, gives values $> 1$ when $\\sum d^2 > 0$ - Option (c): Missing $n$ in denominator — incorrect - Option (d): Uses $n(n^2+1)$ — incorrect denominator The correct formula is Option (a): $r_s = 1 - \\frac{6\\sum d^2}{n(n^2-1)}$ Note: The given `correct_option` says 'd', but Option A is the standard and correct Spearman's formula. Hence, **Option A** is the correct answer.

Correlation and RegressionMCQPYQ Jun 23Question 3678 of 188

All Questions

Spearman's rank correlation coefficient $\displaystyle r_s$ is given by

Options

\displaystyle 1 - \\frac{6 \\sum d^2}{n(n^2 - 1)}

\displaystyle 1 + \\frac{6 \\sum d^2}{n(n^2 - 1)}

\displaystyle 1 - \\frac{6 \\sum d^2}{n^2 - 1}

\displaystyle 1 - \\frac{6 \\sum d^2}{n(n^2 + 1)}

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Correct Answer

✅ Option a — $\displaystyle 1 - \\frac{6 \\sum d^2}{n(n^2 - 1)}$

All Options:

A $\displaystyle 1 - \\frac{6 \\sum d^2}{n(n^2 - 1)}$
B $\displaystyle 1 + \\frac{6 \\sum d^2}{n(n^2 - 1)}$
C $\displaystyle 1 - \\frac{6 \\sum d^2}{n^2 - 1}$
D $\displaystyle 1 - \\frac{6 \\sum d^2}{n(n^2 + 1)}$

Detailed Solution & Explanation

**Spearman's Rank Correlation Coefficient Formula:** Spearman's rank correlation coefficient is:

r_s = 1 - \\frac{6\\sum d_i^2}{n(n^2-1)}

where: -

\displaystyle d_i = R_{1i} - R_{2i}

= difference in ranks of the

\displaystyle i

-th pair -

\displaystyle n

= number of pairs of observations **Verification of other options:** - Option (b): Uses

\displaystyle +

sign — incorrect, gives values

\displaystyle > 1

when

\displaystyle \\sum d^2 > 0

- Option (c): Missing

\displaystyle n

in denominator — incorrect - Option (d): Uses

\displaystyle n(n^2+1)

— incorrect denominator The correct formula is Option (a):

\displaystyle r_s = 1 - \\frac{6\\sum d^2}{n(n^2-1)}

Note: The given `correct_option` says 'd', but Option A is the standard and correct Spearman's formula. 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.

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Correlation vs Regression: Statistics for CA Foundation

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Spearman's rank correlation coefficient rs\displaystyle r_srs​ is given by