Weighted Mean

What is a weighted mean?

A weighted mean gives different importance to different values. Instead of treating all values equally, each value is multiplied by its weight:

$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$

Step-by-step

| Component | Score ($x_i$) | Weight ($w_i$) | $w_i \times x_i$ | |-----------|--------|--------|----------| | Homework | 85 | 20% = 0.20 | 17.0 | | Midterm | 78 | 30% = 0.30 | 23.4 | | Final | 92 | 50% = 0.50 | 46.0 | | Total | | 1.00 | 86.4 |

$\bar{x}_w = \frac{17.0 + 23.4 + 46.0}{1.00} = 86.4$

Compare: Simple mean = $(85 + 78 + 92)/3 = 85.0$. The weighted mean (86.4) is higher because the best score (92) has the highest weight (50%).

When to use weighted mean

• Course grades where different assignments count differently.
• Stock indices where larger companies have more weight.
• GPA calculation where more credit-hour courses count more.

Try it in the visualization

Enter scores and weights. The weighted mean is computed. A bar chart shows how each component contributes to the final average, with bar widths proportional to weights.