Now add the entries in each column to find [tex]\sum x_{i}[/tex] and [tex]\sum x_{i}^2[/tex].

[tex]
\[
\begin{array}{cccc}
x_{i} & x_{i}^2 & x_{i} & x_{i}^2 \\
\hline
71.1 & 5055.21 & 82.5 & 6806.25 \\
68.9 & 4747.21 & 80.7 & 6512.49 \\
79.8 & 6368.04 & 71.9 & 5169.61 \\
66.9 & 4475.61 & 64.3 & 4134.49 \\
84.3 & 7106.49 & 69.2 & 4788.64 \\
77.7 & 6037.29 & 60.7 & 3684.49 \\
56.5 & 3192.25 & & \\
\hline
& & \sum x_{i}=\square & \sum x_{i}^2=\square \\
\hline
\end{array}
\]
[/tex]

(Type integers or decimals. Do not round.)

To solve the problem of finding the sums [tex]\(\sum x_i\)[/tex] and [tex]\(\sum x_i^2\)[/tex], you'll need to add the entries in each column separately. Here’s how you do it step by step:

1. Sum of [tex]\(x_i\)[/tex]:
- Look at the first column of numbers:
[tex]\[
71.1, 68.9, 79.8, 66.9, 84.3, 77.7, 56.5
\][/tex]
- Add them together:
[tex]\[
71.1 + 68.9 + 79.8 + 66.9 + 84.3 + 77.7 + 56.5 = 505.2
\][/tex]

2. Sum of [tex]\(x_i^2\)[/tex]:
- Look at the numbers in the fourth column (the squared values):
[tex]\[
5055.21, 4747.21, 6368.04, 4475.61, 7106.49, 6037.29, 3192.25
\][/tex]
- Add these values together:
[tex]\[
5055.21 + 4747.21 + 6368.04 + 4475.61 + 7106.49 + 6037.29 + 3192.25 = 36982.1
\][/tex]

These calculations give you the results:
- The sum of [tex]\(x_i\)[/tex] is [tex]\(505.2\)[/tex].
- The sum of [tex]\(x_i^2\)[/tex] is [tex]\(36982.1\)[/tex].

These are the totals for each column based on the provided data.