Let's proceed step-by-step to compute the sum of the squares of each measurement given.
First, label the measurements as follows:
- [tex]\( x_1 = 6 \)[/tex]
- [tex]\( x_2 = 7 \)[/tex]
- [tex]\( x_3 = 9 \)[/tex]
- [tex]\( x_4 = 20 \)[/tex]
We need to calculate:
[tex]\[
\sum_{i=1}^4 (x_i)^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2
\][/tex]
Substitute the values of [tex]\( x_1, x_2, x_3, \)[/tex] and [tex]\( x_4 \)[/tex]:
[tex]\[
6^2 + 7^2 + 9^2 + 20^2
\][/tex]
Now square each measurement:
[tex]\[
6^2 = 36
\][/tex]
[tex]\[
7^2 = 49
\][/tex]
[tex]\[
9^2 = 81
\][/tex]
[tex]\[
20^2 = 400
\][/tex]
Next, sum these squared values:
[tex]\[
36 + 49 + 81 + 400
\][/tex]
Add them step-by-step:
[tex]\[
36 + 49 = 85
\][/tex]
[tex]\[
85 + 81 = 166
\][/tex]
[tex]\[
166 + 400 = 566
\][/tex]
Therefore, the sum of the squares of the measurements is:
[tex]\[
\sum_{i=1}^4 (x_i)^2 = 566
\][/tex]
