where x= x - x̅ , y = y - y

where x= x - x̅ , y = y - y S.No x x - x̅ x - =x ( x - x̅ ) = x Y y - y Y – =y (y - y ) =y xy - - - - + - - - - + ∑x = ∑y = ∑xy = Applying in Formula r = ∑xy ∑x ∑y = × = = . r = . , The Car is getting old in years the cost of maintenance is also increasing. The age of Car and its maintenance are positively correlated. Assumed Mean Deviation Method Ex : Find the Karl Pearson coefficient of Correlation between X and Y from the following data: X: Y: x̅ = y̅ = - - Introduction to Statistical Methods and Econometrics Solution: Formula for Assumed Mean Deviation method. r = S.No X Y (X-A)=dx (Y-A)=dy dx2 dy2 Dxdy - - - - - - N= ∑X= ∑Y= ∑(X-A)= ∑(Y-A)= ∑dx = ∑dy = ∑dxdy= N ∑ dxdy − ( ∑ dx ) ( ∑ dy ) N ∑ dx − ( ∑ dx ) N ∑ dy − ( ∑ dy ) y = ∑Y = = N Take the assumed values A = & B = therefore dx = X – A Þ X – and dy = Y- A Þ Y – ∴ r = N ∑ dxdy − ( ∑ dx ) ( ∑ dy ) N ∑ dx − ( ∑ dx ) N ∑ dy − ( ∑ dy ) = × − × × − ( ) × − ( ) = − − = = ( . ) ( . ) = . = . r = . There exists a positive high correlation between X and Y x̅= ∑X = = N