Question

For the data

x :	4	7	8	3	4
y :	5	8	6	3	5

the Karl Pearson coefficient is

• A. $\frac{63}{\sqrt{94 \times 66}}$
• B. 63
• C. $\frac{63}{\sqrt{94}}$
• D. $\frac{63}{\sqrt{66}}$

Answer 1

Answer: (A)

$\frac{63}{\sqrt{94 \times 66}}$

Answer 2

Construct the following table taking $A = 5$ and $B = 5$.

xi	yi	ui= $0.8 = \sqrt{0.2 \times b_{yx}} \Rightarrow b_{yx} = \frac{0.64}{0.2} = 3.2$ – 5	vi= yi – 5	ui2	vi2	uivi
4 7 8 3 4	5 8 6 3 5	– 1 2 3 – 2 – 1	0 3 1 – 2 0	1 4 9 4 1	0 9 1 4 0	0 6 3 4 0
Total		1	2	19	14	13

∴ $r ( X , Y ) = \frac { 13 - \frac { 1 \times 2 } { 5 } } { \sqrt { 19 - \frac { 1 ^ { 2 } } { 5 } } \sqrt { 14 - \frac { 4 } { 5 } } }$ $\bar{x} = \frac{n_{1}{\bar{x}}_{1} + n_{2}{\bar{x}}_{2}}{n_{1} + n_{2}}$