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Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation4 Marks
Question
Find Karl Pearson’s correlation coefficient if:$\text{N}=50,\Sigma\text{x}=75,\Sigma\text{Y}=80,\Sigma\text{X}^2=130,$
$\Sigma\text{Y}^2=140\ \text{and }\Sigma\text{xy}=128.$
✓

Answer

Using Product Moment Methode:$\text{r}=\frac{\text{N}\Sigma\text{XY}-(\Sigma\text{X})(\Sigma\text{Y})}{\sqrt{\text{N}\Sigma\text{X}^2-(\Sigma\text{X})^ 2}.\sqrt{\text{N}\Sigma\text{Y}^2-(\Sigma\text{Y})^2}}$
$=\frac{50\times128-(75)(80)}{\sqrt{50\times130-(75)^2}\sqrt{50\times140-(80)^2}} $
$=\frac{6400-6000}{\sqrt{6500-5625}\sqrt{7000-6400}}$
$=\frac{400}{\sqrt{875}\sqrt{600}}=\frac{400}{29.58\times24.49}$
$=\frac{400}{724.41}=0.55$

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