Question

the coordinate 6 has a weight of 2, the coordinate 9 has a weight of 2, and the coordinate 15 has a weight of 1. find the weighted average. the weighted average is \square.

Explanation:

Step1: Recall weighted average formula

The formula for weighted average is $\frac{\sum (x_i \cdot w_i)}{\sum w_i}$, where $x_i$ are the values and $w_i$ are their corresponding weights.

Step2: Calculate the numerator (sum of products)

For $x_1 = 6$, $w_1 = 2$: $6\times2 = 12$
For $x_2 = 9$, $w_2 = 2$: $9\times2 = 18$
For $x_3 = 15$, $w_3 = 1$: $15\times1 = 15$
Sum of products: $12 + 18 + 15 = 45$

Step3: Calculate the denominator (sum of weights)

Sum of weights: $2 + 2 + 1 = 5$

Step4: Compute weighted average

Weighted average = $\frac{45}{5} = 9$

Answer:

9