Question

the following is a list of 15 measurements.
-79, 37, 13, 42, 93, -34, 57, 73, 59, 67, 57, -22, -94, -24, -14
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suppose that these 15 measurements are respectively labeled ( x_1,x_2,cdots,x_{15} ). (thus, -79 is labeled ( x_1 ), 37 is labeled ( x_2 ), and so on.) compute the following.
sum_{i = 1}^{15}25x_i

Explanation:

Step1: Use the property of summation

We know that \(\sum_{i = 1}^{n}ax_{i}=a\sum_{i = 1}^{n}x_{i}\). Here \(a = 25\) and \(n=15\). So \(\sum_{i = 1}^{15}25x_{i}=25\sum_{i = 1}^{15}x_{i}\).

Step2: Calculate \(\sum_{i = 1}^{15}x_{i}\)

\(\sum_{i = 1}^{15}x_{i}=-79 + 37+13 + 42+93-34 + 57+73+59+67+57-22-94-24-14\)

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Step3: Calculate \(25\sum_{i = 1}^{15}x_{i}\)

Since \(\sum_{i = 1}^{15}x_{i}=231\), then \(25\sum_{i = 1}^{15}x_{i}=25\times231 = 5775\)

Answer:

\(5775\)