To solve the given problem, we need to find the sum of the measurements divided by 11, rounded to at least two decimal places. Let's break down the steps involved in solving this:
1. Identify the measurements:
We have the following data points:
[tex]\[
58, -62, 40, 57, -92, -51, 51, -16, -55, -74, 8, 65, -89, -42
\][/tex]
These measurements are labeled [tex]\(x_1, x_2, \ldots, x_{14}\)[/tex]:
[tex]\[
x_1 = 58, \, x_2 = -62, \, x_3 = 40, \, x_4 = 57, \, x_5 = -92, \, x_6 = -51, \, x_7 = 51, \, x_8 = -16, \, x_9 = -55, \, x_{10} = -74, \, x_{11} = 8, \, x_{12} = 65, \, x_{13} = -89, \, x_{14} = -42
\][/tex]
2. Divide each measurement by 11 and sum them up:
We need to compute:
[tex]\[
\sum_{i=1}^{14} \frac{x_i}{11}
\][/tex]
Breaking it down:
[tex]\[
\frac{58}{11} + \frac{-62}{11} + \frac{40}{11} + \frac{57}{11} + \frac{-92}{11} + \frac{-51}{11} + \frac{51}{11} + \frac{-16}{11} + \frac{-55}{11} + \frac{-74}{11} + \frac{8}{11} + \frac{65}{11} + \frac{-89}{11} + \frac{-42}{11}
\][/tex]
3. Sum up the results:
The sum of the fractions is calculated numerically as:
[tex]\[
-18.363636363636367
\][/tex]
4. Round the sum to at least two decimal places:
Rounding [tex]\(-18.363636363636367\)[/tex] to two decimal places:
[tex]\[
-18.36
\][/tex]
Therefore, the final answer, after rounding to at least two decimal places, is:
[tex]\[
-18.36
\][/tex]
So, the sum of the given measurements divided by 11 is approximately [tex]\(-18.36\)[/tex].
