Question

the following is a list of 10 measurements. -51, 6, 15, -70, -77, 30, -46, -42, 19, -54 suppose that these 10 measurements are respectively labeled $x_1,x_2,cdots,x_{10}$. (thus, -51 is labeled $x_1$, 6 is labeled $x_2$, and so on.) compute the following. $sum_{i = 1}^{10}\frac{x_i}{49}$ round your answer to at least two decimal places.

Explanation:

Step1: Recall the sum - notation property

The sum $\sum_{i = 1}^{10}\frac{x_i}{49}=\frac{1}{49}\sum_{i = 1}^{10}x_i$.

Step2: Calculate the sum of the measurements

$\sum_{i = 1}^{10}x_i=-51 + 6+15-70-77 + 30-46-42+19-54$
$=(-51+6 + 15)+(-70-77)+(30)+(-46-42)+(19-54)$
$=(-30)+(-147)+30+(-88)+(-35)$
$=-30 - 147+30-88-35$
$=-260$.

Step3: Calculate the final result

$\frac{1}{49}\sum_{i = 1}^{10}x_i=\frac{-260}{49}\approx - 5.31$.

Answer:

$-5.31$