It looks like you're calculating the weighted mean (or average) based on the given values $x_1, x_2, x_3, x_4, x_5$ and their corresponding weights $w_1, w_2, w_3, w_4, w_5$.

The formula for the weighted mean $\bar{x}$ is:

$\bar{x} = \frac{\sum (x_i \cdot w_i)}{\sum w_i}$

Substituting the values into the formula:

$\bar{x} = \frac{(2.5 \cdot 3) + (3 \cdot 3) + (1 \cdot 3) + (3 \cdot 3) + (2 \cdot 8)}{3 + 3 + 3 + 3 + 8}$

Let me calculate that.The weighted mean $\bar{x}$ is approximately 2.225.

Would you like further clarification or details on this?

Here are 5 related questions to explore further:

1. What is the difference between a weighted mean and a simple mean?
2. How do changing weights affect the result of the weighted mean?
3. Can you explain the significance of using weights in averaging data?
4. How would the result change if one of the weights was significantly larger than the others?
5. In what real-world situations would you apply a weighted mean?

Tip: When the weights are all equal, the weighted mean becomes the same as the simple arithmetic mean.