Question: Using the data below, answer the following questions using a table format.

X_i 4 6 3 7

y_i 5 2 -1 4 .

\(\,\,\,\,\text{a}\text{. }\sum\limits_{i=1}^{4}{{{x}_{i}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{b}.\,\,\,\sum\limits_{i=1}^{4}{{{y}_{i}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{c}.\,\,\,\sum\limits_{i=1}^{4}{{{x}_{i}}{{y}_{i}}}\,\,\,\,\,\,\,\,\,\,\) \(\,\text{d}\text{. Show that }\,\,\,\sum\limits_{i=1}^{4}{{{x}_{i}}}\,.\,\sum\limits_{i=1}^{4}{{{y}_{i}}}\,\ne \,\sum\limits_{i=1}^{4}{{{x}_{i}}{{y}_{i}}}\,\)

\(\,\,\,\text{e}\text{. }\sum\limits_{i=1}^{4}{x_{i}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{f}.\,\,\,\sum\limits_{i=1}^{4}{y_{i}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\text{g}.\,\,\,{{\left( \sum\limits_{i=1}^{4}{{{x}_{i}}{{y}_{i}}} \right)}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\text{h}\text{. Show that }\,\,\,\sum\limits_{i=1}^{4}{x_{i}^{2}}\,\ne \,{{\left( \sum\limits_{i=1}^{4}{{{x}_{i}}} \right)}^{2}}\,\)

\(\,\,\,\,\text{i}\text{. Show}\,\,\text{that}\,\,\,\,\sum\limits_{i=1}^{4}{({{x}_{i}}}-\,\bar{x}\,)\,\,\,=\,\,\,\sum\limits_{i=1}^{4}{({{y}_{i}}}-\,\bar{y}\,)\,\,=\,\,\,0\,\,\,\,\,\)