Question

Match List - I with List II.

• A. A-I, B-II, C-III, D-IV
• B. A-I, B-II, C-IV, D-III
• C. A-II, B-I, C-III, D-IV
• D. A-II, B-I, C-IV, D-III

Hint:

Logic Tip: Spearman's formula always contains $6\Sigma d^2$ while probable error includes factor $0.6745$.

Answer 1

The Correct Option is A

Step 1:
Karl Pearson's coefficient formula is: \[ r=\frac{\Sigma xy}{\sqrt{\Sigma x^2 \Sigma y^2}} \] Thus: \[ A \rightarrow I \]

Step 2:
Spearman's rank correlation formula is: \[ 1-\frac{6\Sigma d^2}{n(n^2-1)} \] Thus: \[ B \rightarrow II \]

Step 3:
\[ \text{Probable Error}=0.6745 \times \frac{1-r^2}{\sqrt{n}} \] \[ \text{Standard Error}=\frac{1-r^2}{\sqrt{n}} \] Thus: \[ C \rightarrow III \] \[ D \rightarrow IV \]

Step 4:
Final matching is: \[ A-I,\; B-II,\; C-III,\; D-IV \] Hence, the correct answer is: \[ \boxed{\text{(1) A-I, B-II, C-III, D-IV}} \]