Question

Two numbers within the bracket denote the ranks of 10 students of a class in two subjects

(1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1). The rank of correlation coefficient is

• A. 0
• B. – 1
• C. 1
• D. 0.5

Answer 1

Answer: (B)

– 1

Answer 2

Rank correlation coefficient is $r = 1 - 6.\frac{{\sum_{}^{}d}^{2}}{n(n^{2} - 1)}$,

Where $d = y - x$ for pair $(x,y)$

$\therefore$ $\sum d^{2} = 9^{2} + 7^{2} + 5^{2} + 3^{2} + 1^{2} + ( - 1)^{2} + ( - 3)^{2} + ( - 5)^{2} + ( - 7)^{2} + ( - 9)^{2} = 330$Also $n = 10$; $\therefore$ $r = 1 - \frac{6 \times 330}{10(100 - 1)} = - 1$.