Question

Calculate Karl Pearson's coefficient of correlation, between the age and weight of children.

Age (years)	1	2	3	4	5
Weight (kg)	3	4	6	7	10

Answer 1

Age X	Deviation $\mathit{x}\mathit{=}\mathit{X}\mathit{-}\overline{\mathit{X}}$	Square of deviation x2	Weight Y	Deviation $\mathit{y}\mathit{=}\mathit{Y}\mathit{-}\overline{\mathit{Y}}$	Square of deviation y2	xy
1 2 3 4 5	−2 −1 0 1 2	4 1 0 1 4	3 4 6 7 10	−3 −2 0 1 4	9 4 0 1 16	6 2 0 1 8
Σx = 15		Σx2 = 10	ΣY = 30		Σy2 = 30	Σxy= 17

$$\begin{gathered} \overline{\mathrm{X}}=\frac{\mathrm{\Sigma X}}{\mathrm{N}}=\frac{15}{5}=3 \\ \overline{\mathrm{Y}}=\frac{\mathrm{\Sigma Y}}{\mathrm{N}}=\frac{30}{5}=6 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2\times \mathrm{\Sigma }{y}^2}} \\ \mathrm{or},r=\frac{17}{\sqrt{10\times 30}} \\ \mathrm{or},r=\frac{17}{\sqrt{300}} \\ \mathrm{or},r=\frac{17}{17.32} \\ \Rightarrow r=+0.98 \end{gathered}$$

Thus, the coefficient of correlation between the age and weight of children is +0.98.