Sure! Let's compute the sum of the squares of the given measurements step-by-step.
Given measurements:
[tex]\[ x_1 = 9, \, x_2 = 11, \, x_3 = 10, \, x_4 = 15, \, x_5 = 13 \][/tex]
We want to compute the sum of the squares of these measurements, which is denoted by:
[tex]\[ \sum_{i=1}^5 (x_i)^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 \][/tex]
Calculating the square of each measurement:
[tex]\[ x_1^2 = 9^2 = 81 \][/tex]
[tex]\[ x_2^2 = 11^2 = 121 \][/tex]
[tex]\[ x_3^2 = 10^2 = 100 \][/tex]
[tex]\[ x_4^2 = 15^2 = 225 \][/tex]
[tex]\[ x_5^2 = 13^2 = 169 \][/tex]
Now, we add these squared values together:
[tex]\[ 81 + 121 + 100 + 225 + 169 \][/tex]
Adding these numbers step-by-step:
[tex]\[ 81 + 121 = 202 \][/tex]
[tex]\[ 202 + 100 = 302 \][/tex]
[tex]\[ 302 + 225 = 527 \][/tex]
[tex]\[ 527 + 169 = 696 \][/tex]
Thus, the sum of the squares of the measurements is:
[tex]\[ \sum_{i=1}^5 (x_i)^2 = 696 \][/tex]
So, the final result is:
[tex]\[ 696 \][/tex]
