Question

please help me solve ​

Answer 1

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$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$

Solution 1):-

We construct the table of values as under :

$\begin{array}{|c|c|c|c|c|c|c|} \hline \\ \rm X & \rm Y & \rm u= X - A ( A =65) & \rm v= Y - B (B =65 ) & \rm w & \rm u^{2} & \rm v^{2} \\ \\ \hline 65 & 67 & 0 & 2 & 0 & 0 & 4 \\ 66 & 68 & 1 & 3 & 3 & 1 & 9 \\ 67 & 65 & 2 & 0 & 0 & 4 & 0 \\ 67 & 68 & 2 & 3 & 6 & 4 & 9 \\ 68 & 72 & 3 & 7 & 21 & 9 & 49 \\ 69 & 72 & 4 & 7 & 28 & 16 & 49 \\ 70 & 69 & 5 & 4 & 20 & 25 & 16 \\ 72 & 71 & 7 & 6 & 42 & 49 & 36 \\ \hline \\ & & \rm \Sigma u=24 & \rm \Sigma v=32 & \rm\Sigma u v=120 & \rm \Sigma u^{2}=108 & \rm \Sigma v^{2}=172 \\ \\ \hline \end{array}$

$\begin{aligned} \text { By formula, } \rm r & \rm=\frac{\Sigma u v-\frac{1}{n} \Sigma u \Sigma v}{\sqrt{\Sigma u^{2}-\frac{1}{n}(\Sigma u)^{2}} \sqrt{\Sigma v^{2}-\frac{1}{n}(\Sigma v)^{2}}} \\ \\ & =\frac{120-\frac{1}{8} \times 24 \times 32}{\sqrt{108-\frac{1}{8} \times 24^{2}} \sqrt{172-\frac{1}{8} \times(32)^{2}}} \\ \\ &=\frac{120-96}{\sqrt{36} \sqrt{44}}\\ \\ &=\frac{24}{6 \sqrt{44}}\\ \\ &=\frac{4}{\sqrt{44}}\\ \\ &=\frac{2}{\sqrt{11}}\\ \\ &=0.6030 \end{aligned}$