Question

Calculate coefficient of correlation by Pearson's method between the density of population and death rate.

Cities	:	A	B	C	D	E	F
Density	:	200	500	400	700	600	300
Death rate	:	10	16	14	20	17	13

Answer 1

Density (X)	Death rate (Y)	$\left(\mathit{X}\mathit{-}\overline{\mathit{X}}\right)$ x	x2	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ y	y2	xy
200	10	−250	62500	−5	25	1250
500	16	50	2500	1	1	50
400	14	−50	2500	−1	1	50
700	20	250	62500	5	25	1250
600	17	150	22500	2	4	300
300	13	−150	22500	−2	4	300
ƩX = 2700	ƩY =90		Ʃx2 =175000		Ʃy2 =60	Ʃxy =3200

N = 6

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{2700}{6}=450 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{90}{6}=15 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\sqrt{\mathrm{\Sigma }{y}^2}}=\frac{3200}{\sqrt{175000}\sqrt{60}} \\ =\frac{3200}{418.33\times 7.74} \\ =0.988 \end{gathered}$$

Thus, there exists high positive correlation between density of population and death rate.