The problem in the image involves computing the sum of squared values for five given measurements using summation notation. Specifically, we are asked to compute the following sum:

$\sum_{i=1}^{5} x_i^2$

Where $x_1, x_2, x_3, x_4, x_5$ represent the following measurements:

$x_1 = 14, \quad x_2 = 19, \quad x_3 = 16, \quad x_4 = 5, \quad x_5 = 19$

To compute the sum of their squares:

$\sum_{i=1}^{5} x_i^2 = 14^2 + 19^2 + 16^2 + 5^2 + 19^2$

Let's calculate each square:

$14^2 = 196, \quad 19^2 = 361, \quad 16^2 = 256, \quad 5^2 = 25, \quad 19^2 = 361$

Now, summing these results:

$196 + 361 + 256 + 25 + 361 = 1199$

So, the value of the summation is:

$\boxed{1199}$

Would you like further explanation on any of the steps or any additional questions related to this? Here are some follow-up questions you might find helpful:

1. What does summation notation represent and how does it work?
2. How does squaring each term affect the summation process?
3. What are common applications of summation notation in statistics or calculus?
4. How would the result change if the measurements were different?
5. What other types of operations can be performed using summation notation?

Tip: Summation notation is a compact way to represent adding up sequences of numbers or expressions, often useful in statistics, algebra, and calculus.