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Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation6 Marks
Question
Calculate Coefficient of correlation using step deviation method:
X $30$ $40$ $60$ $70$ $100$
Y $90$ $110$ $140$ $150$ $160$
✓

Answer

$X$ $dx = X - A$ $dx'$ $dx'^2$ $Y$ $dy = Y - A$ $dy'$ $dy'^2$ $dx'.dy'$
$30$ -30 -3 9 90 -50 -5 25 15
40 $-20$ -2 4 110 -30 -3 9 6
60 0 0 0 140 0 0 0 0
70 10 1 1 150 10 1 1 1
100 40 4 16 160 20 2 4 8
$\Sigma\text{X}=300\ \text{N}=5$   $\Sigma\text{dx}'=0$ $\Sigma\text{dx}'^2=30$     $\Sigma\text{dy}'=-5$ $\Sigma\text{dy}'^2=39$ $\Sigma\text{dx}'\text{dy}'=30$
$\text{r}=\frac{\text{N.}\Sigma\text{dx}'\text{dy'}-(\Sigma\text{dx}')(\Sigma\text{dy'})}{\sqrt{\text{N.}\Sigma\text{dx}'^2-(\Sigma\text{dx}')^2(\sqrt{\text{N.}\Sigma\text{dy}'^2-(\Sigma\text{dy'})^2}}}$
$=\frac{5\times30-(0)(-5)}{\sqrt{5\times30-(0)^2}\sqrt{5\times39-(-5)^2}}$
$=\frac{150}{\sqrt{150}\sqrt{170}}=\frac{150}{12.24\times13.03}=\frac{150}{159.48}=0.94$

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