Question

Two numbers within the bracket denote the ranks of $10$ students of a class in two subjects: $(1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)$, then rank correlation coefficient is

• A. $0$
• B. $1$
• C. $-1$
• D. $0.5$

Answer 1

The correct option is C

$-1$

Explanation for the correct answer.

Find correlation coefficient:

Given: Marks of $10$ students in two subjects $(1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)$

The formula of coefficient of correlation $=1-\frac{6\sum _i{d}^2}{n(n^2-1)}$

$d$ is the difference in marks, $n$ is the number of observations

$\sum _i{d}^2=9^2+7^2+5^2+3^2+1^2+9^2+7^2+5^2+3^2+1^2=330$

$$\begin{gathered} =1-\frac{6\times 330}{10({10}^2-1)} \\ =1-\frac{1980}{990} \\ =1-2 \\ =-1 \end{gathered}$$

Hence option (c) is correct.