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Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation6 Marks
Question
Compute Karl Pearson's coefficient of correlation by direct method and interpret the result:
Marks in Mathematics 15 18 21 24 27
Marks in Accountancy 25 25 27 31 32
✓

Answer

Let X and Y denote marks in Mathematics and Accountancy, respectively.
X $\text{x}(\text{X}-\overline{\text{X}}),\text{X}=21$ $\text{x}^2$ Y $\text{y}(\text{Y}-\overline{\text{Y}})\text{Y}=28$ $\text{y}^2$ xy
15 - 6 36 25 - 3 9 18
18 - 3 9 25 - 3 9 9
21 0 0 27 - 1 1 0
24 3 9 31 3 9 9
27 6 36 32 4 16 24
$\Sigma\text{X}=105$   $\Sigma\text{x}^2=90$ $\Sigma\text{Y}=140$   $\Sigma\text{y}^2=44$ $\Sigma\text{xy}=60$
Here, $\Sigma\text{X}=105,\Sigma\text{Y}=140,\Sigma\text{xy}=60,\Sigma\text{x}^2=90\text{ and }\Sigma\text{y}^2=44$
$\overline{\text{X}}=\frac{\Sigma\text{X}}{\text{n}}=\frac{105}{5}=21$
$\overline{\text{Y}}=\frac{\Sigma\text{Y}}{\text{n}}=\frac{140}{5}=28$
$\text{r}=\frac{\Sigma\text{xy}}{\sqrt{\Sigma\text{x}^2\times\Sigma\text{y}^2}}$
$=\frac{60}{\sqrt{90\times44}}=\frac{60}{\sqrt{3960}}$
$=\frac{60}{62.928}=0.95$
It indicates that there is high degree of positive correlation between marks in Mathematics and Accountancy.

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