Question

Calculate coefficient of correlation, using Karl Pearson's formula based on actual mean value of the series given below.

Year	Index of Industrial Production	Number of Unemployed People in thousand
2010 2011 2012 2013 2014 2015 2016 2017	100 102 104 107 105 112 103 94	11.3 12.4 14.0 11.1 12.3 12.2 19.1 26.4

Answer 1

Index of Industrial Production (X)	Deviation $\mathit{x}\mathit{=}\mathit{X}\mathit{-}\overline{\mathit{X}}$	Square of deviation (x2)	No. of Unemployed People (Y)	Deviation $\mathit{y}\mathbf{=}\mathit{Y}\mathbf{-}\overline{\mathit{Y}}$	Square deviation (y2)	xy
100 102 104 107 105 112 103 94	−3.375 −1.375 0.625 3.625 1.625 8.625 −0.375 −9.375	11.39 1.89 0.39 13.14 2.64 74.39 0.14 87.89	11.3 12.4 14.0 11.1 12.3 12.2 19.1 26.4	−3.55 −2.45 −0.85 −3.75 −2.55 −2.65 4.25 11.55	12.60 6.00 0.72 14.06 6.50 7.02 18.06 133.40	+11.98 +3.37 −.53 −13.59 −4.14 −22.86 −1.59 −108.28
Σx = 827		Σx2 = 191.87	Σy = 118.8		Σy2 = 198.36	Σxy = −135.64

$$\begin{gathered} \overline{\mathrm{X}}=\frac{\mathrm{\Sigma X}}{\mathrm{N}}=\frac{827}{8}=103.375 \\ \overline{\mathrm{Y}}=\frac{\mathrm{\Sigma Y}}{\mathrm{N}}=\frac{118.8}{8}=14.85 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2\times \mathrm{\Sigma }{y}^2}} \\ \mathrm{or},r=\frac{-135.64}{\sqrt{191.87\times 198.36}} \\ \mathrm{or},r=\frac{-135.64}{\sqrt{38059.33}} \\ \mathrm{or},r=\frac{-135.64}{195.09} \\ \Rightarrow r=-0.69 \end{gathered}$$