Question

The data on price and demand for a commodity is given below:

Price (₹)	14	16	17	18	19	20	21	22	23
Demand (kg.)	84	78	70	75	66	67	62	58	60

Calculate the coefficient of correlation between price and demand and comment on its sign and magnitude.

Answer 1

Price (X)	demand (Y)	X2	Y2	XY
14 16 17 18 19 20 21 22 23	84 78 70 75 66 67 62 58 60	196 256 289 324 361 400 441 484 529	7056 6084 4900 5625 4356 4489 3844 3364 3600	1176 1248 1190 1350 1254 1340 1302 1276 1380
$\mathit{\Sigma }\mathit{X}$=170	$\mathit{\Sigma }\mathit{Y}$=620	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=3280	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=43318	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=11516

N = 9

$$\begin{gathered} r=\frac{\mathrm{N\Sigma XY}-\mathrm{\Sigma X\Sigma Y}}{\sqrt{{\mathrm{N\Sigma X}}^2-{\left(\mathrm{\Sigma X}\right)}^2}\sqrt{{\mathrm{N\Sigma Y}}^2-{\left(\mathrm{\Sigma Y}\right)}^2}} \\ \mathrm{or},r=\frac{9\times 11516-170\times 620}{\sqrt{9\times 3280-{\left(170\right)}^2}\sqrt{9\times 43318-{\left(620\right)}^2}} \\ \mathrm{or},r=\frac{-1756}{24.89\times 73.90} \\ \Rightarrow r=-0.954 \end{gathered}$$

Hence, there is a high degree of negative correlation between price and demand.