Question

What is the weighted average of three points on a number line at 5, 10, and 25, with a ratio of 1:2:2 ?(1 point)Responses11 18 10 15

Answer 1

To calculate the weighted average of the points at 5, 10, and 25 with the given weights in the ratio of 1:2:2, we'll use the formula for weighted averages:

\[
\text{Weighted Average} = \frac{\sum (x_i \cdot w_i)}{\sum w_i}
\]

Where \(x_i\) are the points and \(w_i\) are the corresponding weights.

1. **Identify the values and weights:**
- Point 1 (5) has a weight of 1
- Point 2 (10) has a weight of 2
- Point 3 (25) has a weight of 2

2. **Calculate the weighted sums:**
- For point 5: \(5 \cdot 1 = 5\)
- For point 10: \(10 \cdot 2 = 20\)
- For point 25: \(25 \cdot 2 = 50\)

3. **Sum the weighted values:**
\[
5 + 20 + 50 = 75
\]

4. **Sum the weights:**
\[
1 + 2 + 2 = 5
\]

5. **Calculate the weighted average:**
\[
\text{Weighted Average} = \frac{75}{5} = 15
\]

Thus, the weighted average is **15**.