Question

If $X\mathrm{is}3,4,8,6,2,1$ and $Y\text{is}5,3,9,6,9,2$, then the coefficient of correlation will be approximately:

• A. $0.49$
• B. $0.40$
• C. $-0.49$
• D. $-0.40$

Answer 1

The correct option is A

$0.49$

Explanation for the correct option.

$X$	$Y$	$x=\left(X-\overline{X}\right)$	$x^2$	$y=\left(Y-\overline{Y}\right)$	$y^2$	$xy$
$$\begin{gathered} 3 \\ 4 \\ 8 \\ 6 \\ 2 \\ 1 \end{gathered}$$	$$\begin{gathered} 5 \\ 3 \\ 9 \\ 6 \\ 9 \\ 2 \end{gathered}$$	$$\begin{gathered} -1 \\ 0 \\ 4 \\ 2 \\ -2 \\ -3 \end{gathered}$$	$$\begin{gathered} 1 \\ 0 \\ 16 \\ 4 \\ 4 \\ 9 \end{gathered}$$	$$\begin{gathered} -0.67 \\ -2.67 \\ 3.33 \\ 0.33 \\ 3.33 \\ -3.67 \end{gathered}$$	$$\begin{gathered} 0.45 \\ 7.13 \\ 11.09 \\ 0.11 \\ 11.09 \\ 13.47 \end{gathered}$$	$$\begin{gathered} 0.67 \\ 0 \\ 13.32 \\ 0.66 \\ -6.66 \\ 11.01 \end{gathered}$$
$24$	$34$		$34$		$43.34$	$19$

$$\begin{gathered} \overline{X}=\frac{\Sigma X}{N}=4 \\ \overline{Y}=\frac{\Sigma Y}{N}=5.67 \end{gathered}$$

Coefficient of correlation $\left(r_{xy}\right)=\frac{\Sigma xy}{\sqrt{\Sigma x^2\times \Sigma y^2}}$

$\frac{19}{\sqrt{34\times 43.34}}\approx 0.49$

Hence, option A is correct.