Question

Calculate correlation of the following data using Karl Pearson's method:

Series A	112	114	108	124	145	150	119	125	147	150
Series B	200	190	214	187	170	170	210	190	180	181

Answer 1

Series A	$a=A-\overline{A}$	a2	Series B	$b=B-\overline{B}$	b2	ab
112 114 108 124 145 150 119 125 147 150	–17.4 –15.4 –21.4 –5.4 15.6 20.6 –10.4 –4.4 17.6 20.6	302.76 237.16 457.96 29.16 243.36 424.36 108.16 19.36 309.76 424.36	200 190 214 187 170 170 210 190 180 181	10.8 .8 24.8 –2.2 –19.2 –19.2 20.8 .8 –9.2 –8.2	116.64 .64 615.04 4.84 368.64 368.64 432.64 .64 84.64 67.24	–187.92 –12.32 –530.72 11.88 –299.52 –395.52 –216.32 –3.52 –161.92 –168.92
∑A = 1294		∑a2 = 2556.4	∑B = 1892		∑b2 = 2059.6	∑ab = –1964.8

$$\begin{gathered} \mathrm{Mean}\mathrm{of}\mathrm{Series}A\left(\overline{A}\right)=\frac{{\sum }_{}^{}A}{n}=\frac{1294}{10}=129.4 \\ \mathrm{Mean}\mathrm{of}\mathrm{Series}B\left(\overline{B}\right)=\frac{\sum B}{n}=\frac{1892}{10}=189.2 \\ r\mathit{=}\frac{\sum ab}{\sqrt{\sum {a^{\mathit{2}}}_{}\mathit{\times }\sum b^{\mathit{2}}}}=\frac{-1964.8}{\sqrt{2556.4\times 2059.6}}=-0.85 \end{gathered}$$