It seems the text extraction from the image was not successful. I will analyze the image manually based on the visible elements.

You are asked to solve the problem with the given values:

• $X_1 = 1$, $X_2 = -2$, $X_3 = 15$, $X_4 = -4$, $X_5 = 4$
• $Y_1 = -2$, $Y_2 = 10$, $Y_3 = -1$, $Y_4 = 10$, $Y_5 = -7$

And three options are provided for the solution:

• Option a: $\sum_{i=1}^{5} X_i Y_i$
• Option b: $\left( \sum_{i=1}^{4} X_i \right) \left( \sum_{i=1}^{4} Y_i \right)$
• Option c: $\sum_{i=1}^{5} X_i Y_i - \sum_{i=1}^{5} X_i \sum_{i=1}^{5} Y_i$

Let's start by solving each option step by step to find the correct one.Here are the results for the three options:

• Option a: $\sum_{i=1}^{5} X_i Y_i = -105$
• Option b: $\left( \sum_{i=1}^{4} X_i \right) \left( \sum_{i=1}^{4} Y_i \right) = 170$
• Option c: $\sum_{i=1}^{5} X_i Y_i - \left( \sum_{i=1}^{5} X_i \right) \left( \sum_{i=1}^{5} Y_i \right) = -245$

Thus, the correct answer corresponds to option a: -105.

Let me know if you need more details or have questions.

Here are some related questions you could explore:

1. What is the general formula for summation with indices?
2. How does summation work when there are more complex expressions inside?
3. What are the applications of summation in statistics?
4. How would the problem change if the limits of summation were different?
5. What happens to the summation result if all $X_i$ and $Y_i$ are positive?

Tip: Always ensure that you're correctly interpreting the limits of summation to avoid mistakes in calculations.