Question

the following is a list of 4 measurements.
9, 10, 14, 18
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suppose that these 4 measurements are respectively labeled $x_1, x_2, \dots, x_4$. compute the following.
\\(\displaystyle\sum_{i=1}^{4} (x_i)^2\\)

Explanation:

Step1: Identify each \( x_i \)

The measurements are \( x_1 = 9 \), \( x_2 = 10 \), \( x_3 = 14 \), \( x_4 = 18 \).

Step2: Compute each \( (x_i)^2 \)

• \( (x_1)^2 = 9^2 = 81 \)
• \( (x_2)^2 = 10^2 = 100 \)
• \( (x_3)^2 = 14^2 = 196 \)
• \( (x_4)^2 = 18^2 = 324 \)

Step3: Sum the squared values

\( \sum_{i = 1}^{4}(x_i)^2 = 81 + 100 + 196 + 324 \)
\( = 181 + 196 + 324 \)
\( = 377 + 324 \)
\( = 701 \)

Answer:

\( 701 \)