Question

For the data, $x47834andy58635$, then Karl Pearson's coefficient is

• A. $\raisebox{1ex}{$63$}\!\left/ \!\raisebox{-1ex}{$\sqrt{94\times 66}$}\right.$
• B. $63$
• C. $\raisebox{1ex}{$63$}\!\left/ \!\raisebox{-1ex}{$\sqrt{94}$}\right.$
• D. $\raisebox{1ex}{$63$}\!\left/ \!\raisebox{-1ex}{$\sqrt{66}$}\right.$

Answer 1

The correct option is A

$\raisebox{1ex}{$63$}\!\left/ \!\raisebox{-1ex}{$\sqrt{94\times 66}$}\right.$

Explanation for the correct option:

Karl Pearson's coefficient

$\begin{array}{|lllllll|}\hline x_i& y_i& u_i=x_i-5& v_i=y_i-5& {u_i}^2& {v_i}^2& u_i{v}_i\\ 4& 5& -1& 0& 1& 0& 0\\ 7& 8& 2& 3& 4& 9& 6\\ 8& 6& 3& 1& 9& 1& 3\\ 3& 3& -2& -2& 4& 4& 4\\ 4& 5& -1& 0& 1& 0& 0\\ \text{Total}& & 1& 2& 19& 14& 13\\ \hline\end{array}$

${\mathit{r}}_{\mathbf{(}\mathbf{x}\mathbf{,}\mathbf{y}\mathbf{)}}\mathbf{=}\frac{\mathbf{\sum }_{}{\mathbf{u}}_{\mathbf{i}}{\mathbf{v}}_{\mathbf{i}}}{\sqrt{\mathbf{\sum }_{}{\mathbf{\left(}{\mathbf{u}}_{\mathbf{i}}\mathbf{\right)}}^{\mathbf{2}}\mathbf{\times }\mathbf{\sum }_{}{\mathbf{\left(}{\mathbf{v}}_{\mathbf{i}}\mathbf{\right)}}^{\mathbf{2}}}}$

Now put all the value in the above formula;

$\begin{array}{rcl}{r}_{(x,y)}& =& [13-\{(1\times 2)/5\left\}\right]/\left[\sqrt{19-(1^2/5}\right)\times \sqrt{14-(4/5)}]\\ & =& 63/\left[\right(\sqrt{94\times 66}\end{array}$

Hence, option $\left(A\right)$ is correct option