The problem asks to compute the sum of five measurements that are labeled as $x_1, x_2, \dots, x_5$, with the given values of:

$x_1 = 8, \quad x_2 = 10, \quad x_3 = 10, \quad x_4 = 9, \quad x_5 = 18$

We are tasked with calculating the sum of these five values, expressed as:

$\sum_{i=1}^{5} x_i = x_1 + x_2 + x_3 + x_4 + x_5$

Now, let's compute the sum:

$8 + 10 + 10 + 9 + 18 = 55$

So, the sum is:

$\sum_{i=1}^{5} x_i = 55$

Would you like more details or have any questions?

Here are five related questions:

1. How do you calculate the average (mean) of these measurements?
2. What is the variance of these five measurements?
3. Can you compute the standard deviation of this data set?
4. How would you express the sum if there were $n$ measurements?
5. What is the range of this data set?

Tip: When summing multiple numbers, organizing them into smaller groups or using a calculator can minimize errors and speed up the process.