Question

Find out the correlation between the marks in Statistics and marks in Accountancy:

No. of Students	1	2	3	4	5	6	7	8	9	10
Marks in Statistics	20	35	15	40	10	35	30	25	45	30
marks in Accountancy	25	30	20	35	20	25	25	35	35	30

Answer 1

Marks in Statistics (X)	Marks in Accountancy (Y)	X2	Y2	XY
20 35 15 40 10 35 30 25 45 30	25 30 20 35 20 25 25 35 35 30	400 1225 225 1600 100 1225 900 625 2025 900	625 900 400 1225 400 625 625 1225 1225 900	500 1050 300 1400 200 875 750 875 1575 900
$\mathit{\Sigma }\mathit{X}$=285	$\mathit{\Sigma }\mathit{Y}$=280	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=9225	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=8150	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=8425

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},\mathit{}r=\frac{10\times 8425-280\times 285}{\sqrt{10\times 9225-{\left(285\right)}^2}\sqrt{10\times 8150-{\left(280\right)}^2}} \\ \mathrm{or},\mathit{}r=\frac{4450}{105\times 55.67} \\ \Rightarrow r=0.761 \end{gathered}$$

Thus, there exists a high degree of positive correlation between the marks in Statistics and marks in Accountancy.