Sure, let's solve the problem step-by-step.
Given the measurements:
[tex]\[ x_1 = 7, \, x_2 = 13, \, x_3 = 8, \, x_4 = 13 \][/tex]
We need to compute the sum of the squares of these measurements:
[tex]\[ \sum_{i=1}^4 (x_i)^2 \][/tex]
Here are the steps to find this sum:
1. Square each measurement:
[tex]\[
x_1^2 = 7^2 = 49
\][/tex]
[tex]\[
x_2^2 = 13^2 = 169
\][/tex]
[tex]\[
x_3^2 = 8^2 = 64
\][/tex]
[tex]\[
x_4^2 = 13^2 = 169
\][/tex]
2. Sum the squared measurements:
[tex]\[
x_1^2 + x_2^2 + x_3^2 + x_4^2 = 49 + 169 + 64 + 169
\][/tex]
3. Add these values together:
[tex]\[
49 + 169 = 218
\][/tex]
[tex]\[
218 + 64 = 282
\][/tex]
[tex]\[
282 + 169 = 451
\][/tex]
Thus, the sum of the squares of the measurements is:
[tex]\[ \sum_{i=1}^4 (x_i)^2 = 451 \][/tex]
So, the final result is:
[tex]\[ 451 \][/tex]
