Question

Please teach me on how to answer this question. (addmath question)

Answer 1

We know that
`\overline{x}=8` so:

`image`

We want to calculate:

`\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}`