Question

10 students obtained following ranks in their mathematics and statistics examinations. Find out the extent to which the knowledge of students is correlated in the two subjects.

Rank in Statistics	1	2	3	4	5	6	7	8	9	10
Rank in Mathematics	2	4	1	5	3	9	7	10	6	8

Answer 1

Rank in statistics (R1)	Rank in Mathematics (R2)	D = R1 − R2	D2
1 2 3 4 5 6 7 8 9 10	2 4 1 5 3 9 7 10 6 8	−1 −2 2 −1 2 −3 0 −2 3 2	1 4 4 1 4 9 0 4 9 4
N = 10			ΣD2= 40

$$\begin{gathered} r_k=1-\frac{6{\mathrm{\Sigma D}}^2}{{\mathrm{N}}^3-\mathrm{N}} \\ \mathrm{or},r_k=1-\frac{6\times 40}{{\left(10\right)}^3-10} \\ \mathrm{or},r_k=1-\frac{240}{1000-10} \\ \mathrm{or},r_k=1-\frac{240}{990} \\ \mathrm{or},r_k=1-.24 \\ \Rightarrow r_k=+0.76 \end{gathered}$$

Thus, there is a high degree of positive correlation between the marks of the students in statistics and mathematics.