Question

Find Karl Pearson's coefficient for the following data:

Marks in English	45	70	65	30	90	40	50	75	85	60
Marks in Maths	35	90	70	40	95	40	60	80	80	50

Answer 1

Marks in English (X)	Marks in Maths (Y)	X2	Y2	XY
45 70 65 30 90 40 50 75 85 60	35 90 70 40 95 40 60 80 80 50	2025 4900 4225 900 8100 1600 2500 5625 7225 3600	1225 8100 4900 1600 9025 1600 3600 6400 6400 2500	1575 6300 4550 1200 8550 1600 3000 6000 6800 3000
$\Sigma X$=610	$\Sigma Y$=640	$\Sigma X^2$=40700	$\Sigma Y^2$=45350	$\Sigma XY$=42575

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{10\times 42575-610\times 640}{\sqrt{10\times 40700-{\left(610\right)}^2}\sqrt{10\times 45350-{\left(640\right)}^2}} \\ \mathrm{or},r=\frac{35350}{186.81\times 209.52} \\ \Rightarrow \mathrm{r}=0.9031 \end{gathered}$$

Hence, Karl Pearson's coefficient is 0.9031.