To calculate the weighted mean:
\[ WM = \frac{\sum{(w_i \cdot x_i)}}{\sum{w_i}} \]
Where:
A weighted mean, also known as a weighted average, is a method of calculating an average where some values contribute more than others. In a standard mean, all values are treated equally and contribute the same amount to the final average. A weighted mean takes into account the importance, or weight, of each value, giving a more accurate representation of the data set when some values are more significant than others.
Let's assume the following values and weights:
Using the formula:
\[ WM = \frac{(1 \cdot 10) + (2 \cdot 20) + (3 \cdot 30)}{1 + 2 + 3} = \frac{10 + 40 + 90}{6} = \frac{140}{6} \approx 23.33 \]
The weighted mean is approximately 23.33.
