Question

The data on price and quantity purchased relating to a commodity for 10 months are given below:Calculate coefficient of correlation between price and quantity.

Price (₹)	10	14	12	11	9	7	15	16	18	20
Quantity (kg.)	25	20	30	32	35	40	19	16	12	10

Answer 1

Price (X)	Quantity (Y)	X2	Y2	XY
10 14 12 11 9 7 15 16 18 20	25 20 30 32 35 40 19 16 12 10	100 196 144 121 81 49 225 256 324 400	625 400 900 1024 1225 1600 361 256 144 100	250 280 360 352 315 280 285 256 216 200
$\mathit{\Sigma }\mathit{X}$=132	$\mathit{\Sigma }\mathit{Y}$=239	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=1896	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=6635	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=2794

N = 10

$$\begin{gathered} r=\frac{N\Sigma \mathrm{XY}-\Sigma \mathrm{X\Sigma Y}}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{10\times 2794-132\times 239}{\sqrt{10\times 1896-{\left(132\right)}^2}\sqrt{10\times 6635-{\left(239\right)}^2}} \\ \mathrm{or},r=\frac{-3608}{39.19\times 96.06} \\ \Rightarrow r=-0.958 \end{gathered}$$

Thus, the coefficient of correlation between price and quantity is -0.958.