the coordinate 3 has a weight of 2, and the coordinate 8 has a weight of 3. 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 $x_i$ are the values and $w_i$ are their corresponding weights. Here, $x_1 = 3$, $w_1=2$, $x_2 = 8$, and $w_2 = 3$.

Step2: Calculate the numerator

$\sum_{i = 1}^{2}w_ix_i=w_1x_1 + w_2x_2=2\times3+3\times8=6 + 24=30$.

Step3: Calculate the denominator

$\sum_{i = 1}^{2}w_i=w_1 + w_2=2 + 3=5$.

Step4: Calculate the weighted average

$\bar{x}=\frac{\sum_{i = 1}^{2}w_ix_i}{\sum_{i = 1}^{2}w_i}=\frac{30}{5}=6$.

Answer:

6