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The following is a list of 4 measurements:

[tex]\[
7, 13, 8, 13
\][/tex]

Suppose that these 4 measurements are respectively labeled [tex]\[ x_1, x_2, \ldots, x_4 \][/tex]. Compute the following:

[tex]\[
\sum_{i=1}^4 \left(x_i\right)^2
\][/tex]



Answer :

GinnyAnswer
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]

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