Question

Find the coefficient of rank correlation between the marks obtained in Mathematics and those in Statistics by 10 students of a class.

Marks in Mathematics	12	18	32	18	25	24	25	40	38	22
Marks in Statistics	16	15	28	16	24	22	25	36	34	19

Answer 1

Marks in Maths	Marks in Statistics	R1	R2	D = R1−R2	D2
12 18 32 18 25 24 25 40 38 22	16 15 28 16 24 22 25 36 34 19	1 2.5 8 2.5 6.5 5 6.5 10 9 4	2.5 1 8 2.5 6 5 7 10 9 4	-1.5 1.5 0 0 0.5 0 -0.5 0 0 0	2.25 2.25 0 0 0.25 0 0.25 0 0 0
					$\Sigma D^2$=5

Here, N = 10
m₁= m₂ = m₃ = 2

$$\begin{gathered} r_{\mathit{k}}=1-\frac{6\left[{\mathrm{\Sigma D}}^2+{\displaystyle \frac{1}{12}}\left({{\mathrm{m}}_1}^3-{\mathrm{m}}_1\right)+{\displaystyle \frac{1}{12}}\left({{\mathrm{m}}_2}^3-{\mathrm{m}}_2\right)+{\displaystyle \frac{1}{12}}\left({{\mathrm{m}}_3}^3-{\mathrm{m}}_3\right)\right]}{{\mathrm{N}}^3-\mathrm{N}} \\ \mathrm{or},r_{\mathit{k}}=1-\frac{6\left[5+{\displaystyle \frac{1}{12}}\left(8-2\right)+{\displaystyle \frac{1}{12}}\left(8-2\right)+{\displaystyle \frac{1}{12}}\left(8-2\right)\right]}{990} \\ \Rightarrow r_{\mathit{k}}=0.960 \end{gathered}$$

Hence, the value of rank correlation coefficient is 0.960.