To solve the problem of finding the sum of the squares of the given measurements [tex]\(6, 18, 20, 6, 12\)[/tex], we need to follow these steps:
1. List the measurements and label them:
[tex]\( x_1 = 6 \)[/tex]
[tex]\( x_2 = 18 \)[/tex]
[tex]\( x_3 = 20 \)[/tex]
[tex]\( x_4 = 6 \)[/tex]
[tex]\( x_5 = 12 \)[/tex]
2. Square each of these measurements:
[tex]\(x_1^2 = 6^2 = 36\)[/tex]
[tex]\(x_2^2 = 18^2 = 324\)[/tex]
[tex]\(x_3^2 = 20^2 = 400\)[/tex]
[tex]\(x_4^2 = 6^2 = 36\)[/tex]
[tex]\(x_5^2 = 12^2 = 144\)[/tex]
3. Add the squares of these 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]
Substituting the values, we get:
[tex]\[
= 36 + 324 + 400 + 36 + 144
\][/tex]
4. Calculate the sum:
[tex]\[
36 + 324 + 400 + 36 + 144 = 940
\][/tex]
Therefore, the sum of the squares of the given measurements is [tex]\( \boxed{940} \)[/tex].
