To compute the sum of the squares of the given measurements [tex]\( x_1, x_2, \ldots, x_5 \)[/tex], follow these steps:
1. Identify the values of the measurements:
[tex]\[
x_1 = 5, \quad x_2 = 16, \quad x_3 = 6, \quad x_4 = 13, \quad x_5 = 8
\][/tex]
2. Square each individual measurement:
[tex]\[
x_1^2 = 5^2 = 25
\][/tex]
[tex]\[
x_2^2 = 16^2 = 256
\][/tex]
[tex]\[
x_3^2 = 6^2 = 36
\][/tex]
[tex]\[
x_4^2 = 13^2 = 169
\][/tex]
[tex]\[
x_5^2 = 8^2 = 64
\][/tex]
3. Sum the squares of the measurements:
[tex]\[
\sum_{i=1}^5 x_i^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2
\][/tex]
[tex]\[
= 25 + 256 + 36 + 169 + 64
\][/tex]
[tex]\[
= 550
\][/tex]
Therefore, the sum of the squares of the measurements is:
[tex]\[
\boxed{550}
\][/tex]
