We know that [tex] \overline{x}=8 [/tex] so:
[tex] \overline{x}=8\\\\\\\dfrac{\sum\limits_{k=1}^7\,x_k}{7}=8\qquad|\cdot7\\\\\\
\boxed{\sum\limits_{k=1}^7\,x_k=56} [/tex]
We want to calculate:
[tex] \sum\limits_{k=1}^7\,\big(2x_k-3\big)^2=\sum\limits_{k=1}^7\,\big(4x_k^2-12x_k+9\big)=\\\\\\=\sum\limits_{k=1}^7\,4x_k^2-\sum\limits_{k=1}^7\,\big12x_k+\sum\limits_{k=1}^7\,9=4\sum\limits_{k=1}^7\,x_k^2-12\sum\limits_{k=1}^7\,x_k+\sum\limits_{k=1}^7\,9=\\\\\\=4\cdot672-12\cdot56+7\cdot9=2688-672+63=\boxed{2079} [/tex]
