UPHESC Assistant Professor Commerce 19 Apr 2026 Shift 2 Question Paper PDF with Answer Key

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Section	Questions	Marks
Commerce	70	140

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Q1.

If the sum of the squares of rank differences is 6 and there are two variables X and Y with 8 items each, what would be the coefficient of rank correlation ?

यदि रैंक अंतरों के वर्गों का योग 6 हो और दो चर X और Y प्रत्येक में 8 आइटम हों, तो रैंक सहसंबंध गुणांक क्या होगा ?

A1
B0·07
C0·93
D0·67

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Concept: Spearman's rank correlation: $R = 1 - \frac{6 \sum D^{2}}{N (N^{2} - 1)}$ .

Here $\sum D^{2} = 6$ , $N = 8$ , so $N (N^{2} - 1) = 8 \times 63 = 504$ .
$R = 1 - \frac{6 \times 6}{504} = 1 - \frac{36}{504} = 1 - 0.0714 = 0.9286$ .
Rounded, $R \approx 0.93$ .

Short trick: For N = 8 the denominator is always 504; just compute 1 − 6ΣD²/504.

अवधारणा: स्पीयरमैन कोटि सहसंबंध: $R = 1 - \frac{6 \sum D^{2}}{N (N^{2} - 1)}$ ।

यहाँ $\sum D^{2} = 6$ , $N = 8$ , अतः $N (N^{2} - 1) = 8 \times 63 = 504$ ।
$R = 1 - \frac{36}{504} = 1 - 0.0714 = 0.9286$ ।
पूर्णांकित करने पर $R \approx 0.93$ ।

याद रखें: N = 8 के लिए हर सदैव 504 होता है; बस 1 − 6ΣD²/504 निकालें।

UPHESC Assistant Professor CommerceCommerceSpearman's rank correlation

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