Question

Calculate Karl Pearson's Coefficient of Correlation between the sales and expenses of the following 10 firms:

Firms	:	1	2	3	4	5	6	7	8	9	10
Sales(in ₹ '000)	:	50	50	55	60	65	65	65	60	60	50
Expenses (in ₹ '000)	:	11	13	14	16	16	15	15	14	13	13

Answer 1

Sales (X)	Expenses (Y)	$\left(\mathit{X}\mathit{-}\overline{X}\right)$ x	x2	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ y	y2	xy
50	11	−8	64	−3	9	24
50	13	−8	64	−1	1	8
55	14	−3	9	0	0	0
60	16	2	4	2	4	4
65	16	7	49	2	4	14
65	15	7	49	1	1	7
65	15	7	49	1	1	7
60	14	2	4	0	0	0
60	13	2	4	−1	1	−2
50	13	−8	64	−1	1	8
580	140		360		22	70

N = 10

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{580}{10}=58 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{140}{10}=14 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\sqrt{\mathrm{\Sigma }{y}^2}}=\frac{70}{\sqrt{360}\sqrt{22}}=\frac{70}{18.973\times 4.690}=\frac{70}{88.9833} \\ =0.786 \end{gathered}$$

Note: As per the textbook, coefficient of correlation is 0.67. However, as per the above solution coefficient of correlation should be 0.786.