Question

Calculate Karl Pearson's coefficient between the marks (out of 30) in English and Hindi obtained by 10 students.

Marks in English	10	25	13	25	22	11	12	25	21	20
Marks in Hindi	12	22	16	15	18	18	17	23	24	17

Answer 1

Marks in English (X)	Marks in Hindi (Y)	X2	Y2	XY
10 25 13 25 22 11 12 25 21 20	12 22 16 15 18 18 17 23 24 17	100 625 169 625 484 121 144 625 441 400	144 484 256 225 324 324 289 529 576 289	120 550 208 375 396 198 204 575 504 340
$\mathit{\Sigma }\mathit{X}$=184	$\mathit{\Sigma }\mathit{Y}$=182	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=3734	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=3440	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=3470

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\mathrm{\Sigma }Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma \mathrm{Y}\right)}^2}} \\ \mathrm{or},r=\frac{10\times 3470-184\times 182}{\sqrt{10\times 3734-{\left(184\right)}^2}\sqrt{10\times 3440-{\left(182\right)}^2}} \\ \mathrm{or},r=\frac{1212}{59.02\times 35.72} \\ \Rightarrow r=0.574 \end{gathered}$$

Thus, coefficient of correlation = 0.574