To find the value of [tex]\(\sum_{i=1}^4 (x_i)^2\)[/tex] given the measurements [tex]\(x_1 = 7\)[/tex], [tex]\(x_2 = 19\)[/tex], [tex]\(x_3 = 13\)[/tex], and [tex]\(x_4 = 18\)[/tex], we need to compute the sum of the squares of each measurement. Here is a step-by-step solution:
1. Square each of the measurements:
- [tex]\(x_1^2 = 7^2 = 49\)[/tex]
- [tex]\(x_2^2 = 19^2 = 361\)[/tex]
- [tex]\(x_3^2 = 13^2 = 169\)[/tex]
- [tex]\(x_4^2 = 18^2 = 324\)[/tex]
2. Sum these squares together:
[tex]\[
49 + 361 + 169 + 324
\][/tex]
3. Perform the addition:
- First, add 49 and 361: [tex]\(49 + 361 = 410\)[/tex]
- Next, add 410 and 169: [tex]\(410 + 169 = 579\)[/tex]
- Finally, add 579 and 324: [tex]\(579 + 324 = 903\)[/tex]
Therefore, the value of [tex]\(\sum_{i=1}^4 (x_i)^2\)[/tex] is [tex]\(903\)[/tex].
[tex]\[
\boxed{903}
\][/tex]
