Question
Find the weighted average of the numbers 1 and 8, with a weight of two-fifths on the first number and three-fifths on the second number.
5.2
3.5
4.8
1.6
5.2
3.5
4.8
1.6
Answers
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Answered by
GPT-4o mini
To find the weighted average, you can use the formula:
\[
\text{Weighted Average} = \left( w_1 \cdot x_1 + w_2 \cdot x_2 \right) / (w_1 + w_2)
\]
where \( w_1 \) and \( w_2 \) are the weights, and \( x_1 \) and \( x_2 \) are the corresponding values.
In this case:
- \( x_1 = 1 \), \( w_1 = \frac{2}{5} \)
- \( x_2 = 8 \), \( w_2 = \frac{3}{5} \)
Now, we calculate the weighted average:
\[
\text{Weighted Average} = \left( \frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 \right) / \left( \frac{2}{5} + \frac{3}{5} \right)
\]
Calculating the numerator:
\[
\frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 = \frac{2}{5} + \frac{24}{5} = \frac{2 + 24}{5} = \frac{26}{5}
\]
Calculating the denominator:
\[
\frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1
\]
Now, substituting these values back into the weighted average formula gives:
\[
\text{Weighted Average} = \frac{\frac{26}{5}}{1} = \frac{26}{5} = 5.2
\]
So, the weighted average of the numbers 1 and 8 is **5.2**.
\[
\text{Weighted Average} = \left( w_1 \cdot x_1 + w_2 \cdot x_2 \right) / (w_1 + w_2)
\]
where \( w_1 \) and \( w_2 \) are the weights, and \( x_1 \) and \( x_2 \) are the corresponding values.
In this case:
- \( x_1 = 1 \), \( w_1 = \frac{2}{5} \)
- \( x_2 = 8 \), \( w_2 = \frac{3}{5} \)
Now, we calculate the weighted average:
\[
\text{Weighted Average} = \left( \frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 \right) / \left( \frac{2}{5} + \frac{3}{5} \right)
\]
Calculating the numerator:
\[
\frac{2}{5} \cdot 1 + \frac{3}{5} \cdot 8 = \frac{2}{5} + \frac{24}{5} = \frac{2 + 24}{5} = \frac{26}{5}
\]
Calculating the denominator:
\[
\frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1
\]
Now, substituting these values back into the weighted average formula gives:
\[
\text{Weighted Average} = \frac{\frac{26}{5}}{1} = \frac{26}{5} = 5.2
\]
So, the weighted average of the numbers 1 and 8 is **5.2**.
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