Question

the following is a list of 12 measurements. -13, -22, -16, -19, -6, -30, -74, -70, 65, -84, -8, 36 suppose that these 12 measurements are respectively labeled (x_1,x_2,ldots,x_{12}). (thus, -13 is labeled (x_1), -22 is labeled (x_2), and so on.) compute the following. (sum_{i = 1}^{12}10x_i)

Explanation:

Step1: Recall the sum - property

We know that $\sum_{i = 1}^{n}ax_{i}=a\sum_{i = 1}^{n}x_{i}$, where $a$ is a constant. Here $a = 10$ and $n=12$. So $\sum_{i = 1}^{12}10x_{i}=10\sum_{i = 1}^{12}x_{i}$.

Step2: Calculate the sum of the measurements

$\sum_{i = 1}^{12}x_{i}=-13+( - 22)+(-16)+(-19)+(-6)+(-30)+(-74)+(-70)+65+(-84)+(-8)+36$.
\[

$$\begin{align*} \sum_{i = 1}^{12}x_{i}&=(-13-22 - 16-19-6-30-74-70)+(65 + 36-84-8)\\ &=(-250)+( - 11)\\ &=-261 \end{align*}$$

\]

Step3: Calculate the final result

Since $\sum_{i = 1}^{12}10x_{i}=10\sum_{i = 1}^{12}x_{i}$, substituting $\sum_{i = 1}^{12}x_{i}=-261$ into the equation, we get $10\times(-261)=-2610$.

Answer:

$-2610$