the coordinate -6 has a weight of 3, and the coordinate 2 has a weight of 1. find the weighted average…

Explanation:

Step1: Recall weighted - average formula

The formula for the weighted average $\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}$, where $w_i$ is the weight and $x_i$ is the value. Here, $x_1=-6$, $w_1 = 3$, $x_2 = 2$, $w_2=1$.

Step2: Calculate the numerator

$\sum_{i = 1}^{2}w_ix_i=w_1x_1 + w_2x_2=3\times(-6)+1\times2=-18 + 2=-16$.

Step3: Calculate the denominator

$\sum_{i = 1}^{2}w_i=w_1+w_2=3 + 1=4$.

Step4: Calculate the weighted average

$\bar{x}=\frac{-16}{4}=-4$.

Answer:

$-4$