Question

Three points are on a number line at 2, 4, and 8 with weights of 10%, 30%, and 60%.

The weighted average is _

Answer 1

To find the weighted average of the three points on the number line, we can use the formula for the weighted average:

\[
\text{Weighted Average} = \frac{(x_1 \cdot w_1) + (x_2 \cdot w_2) + (x_3 \cdot w_3)}{w_1 + w_2 + w_3}
\]

Where:
- \( x_1, x_2, x_3 \) are the points (2, 4, and 8),
- \( w_1, w_2, w_3 \) are the respective weights (10%, 30%, 60%).

First, convert the weights from percentages to decimals:
- \( w_1 = 0.10 \)
- \( w_2 = 0.30 \)
- \( w_3 = 0.60 \)

Next, plug in the values into the weighted average formula:

\[
\text{Weighted Average} = \frac{(2 \cdot 0.10) + (4 \cdot 0.30) + (8 \cdot 0.60)}{0.10 + 0.30 + 0.60}
\]

Calculating the numerator:

\[
2 \cdot 0.10 = 0.2
\]
\[
4 \cdot 0.30 = 1.2
\]
\[
8 \cdot 0.60 = 4.8
\]

Adding these products together:

\[
0.2 + 1.2 + 4.8 = 6.2
\]

Now, calculate the denominator:

\[
0.10 + 0.30 + 0.60 = 1.00
\]

Now divide the total by the sum of weights:

\[
\text{Weighted Average} = \frac{6.2}{1.00} = 6.2
\]

Thus, the weighted average is **6.2**.