Question

Calculate the correlation coefficient of the marks obtained by 12 students in Mathematics and Statistics and interpret it.

Students	:	A	B	C	D	E	F	G	H	I	J	K	L
Marks (in Maths)	:	50	54	56	59	60	62	61	65	67	71	71	74
Marks ( in Statis.)	:	22	25	34	28	26	30	32	30	28	34	36	40

Answer 1

Maths (X)	Statis. (Y)	$\left(\mathit{X}\mathit{-}\overline{X}\right)$ x	x2	$\left(\mathit{Y}\mathit{-}\overline{Y}\right)$ (y)	y2	xy
50	22	−12.5	156.25	−8.41	70.72	105.12
54	25	−8.5	72.25	−5.41	29.26	45.98
56	34	−6.5	42.25	3.59	12.88	−23.33
59	28	−3.5	12.25	−2.41	5.80	8.43
60	26	−2.5	6.25	−4.41	19.44	11.02
62	30	−0.5	0.25	−0.41	0.168	0.205
61	32	−1.5	2.25	1.59	2.52	−2.38
65	30	2.5	6.25	−.41	0.168	−1.02
67	28	4.5	20.25	−2.41	5.80	−10.84
71	34	8.5	72.25	3.59	12.88	30.51
71	36	8.5	72.25	5.59	31.24	47.51
74	40	11.5	132.25	9.59	91.96	110.28
ƩX = 750	ƩY= 365		Ʃx2 = 595		Ʃy2 = 282.836	Ʃxy = 321.485

N = 12

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{750}{12}=62.5 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{365}{12}=30.41 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ =\frac{321.485}{\sqrt{595}\times \sqrt{282.836}} \\ =\frac{321.485}{24.392\times 16.80} \\ =\frac{321.485}{410.22} \\ =0.783 \end{gathered}$$
Thus, there exists sufficiently high degree of positive correlation marks in Mathematics and marks in Statistics.