Question

Following are the heights and weights of 10 students of a class:

Height (inches)	60	64	68	62	67	69	70	72	65	61
Weight (kg)	50	48	56	65	49	52	57	60	59	47

Calculate the coefficient of correlation by Karl Pearson's method:

Answer 1

Height (X)	Weight (Y)	X2	Y2	XY
60 64 68 62 67 69 70 72 65 61	50 48 56 65 49 52 57 60 59 47	3600 4096 4624 3844 4489 4761 4900 5184 4225 3721	2500 2304 3136 4225 2401 2704 3249 3600 3481 2209	3000 3072 3808 4030 3283 3588 3990 4320 3835 2867
$\mathit{\Sigma }\mathit{X}$=658	$\mathit{\Sigma }\mathit{Y}$=543	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=43444	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=29809	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=35793

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\mathrm{\Sigma }Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma \mathrm{Y}\right)}^2}} \\ \mathrm{or},r=\frac{10\times 35793-658\times 543}{\sqrt{10\times 43444-{\left(658\right)}^2}\sqrt{10\times 29809-{\left(543\right)}^2}} \\ \mathrm{or},r=\frac{636}{38.41\times 56.92} \\ \Rightarrow r=0.29 \end{gathered}$$

Hence, coefficient of correlation is 0.29.