Weighted Average

Statistics
definition

Also known as: weighted mean

Grade 6-8

An average in which different values contribute unequally based on their assigned weights. Used in GPA calculation, financial analysis, polling, and any situation where data points differ in importance.

Definition

An average in which different values contribute unequally based on their assigned weights.

💡 Intuition

Your final grade: exams count 60%, homework 40% — not every assignment counts equally.

🎯 Core Idea

Multiply each value by its weight, sum the products, then divide by the total weight.

Example

Scores 80 (weight 0.4) and 90 (weight 0.6): weighted average = 80×0.4 + 90×0.6 = 86.

Formula

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

🌟 Why It Matters

Used in GPA calculation, financial analysis, polling, and any situation where data points differ in importance.

🚧 Common Stuck Point

Weights don't have to be percentages — any positive numbers work as long as you divide by their sum.

Frequently Asked Questions

What is Weighted Average in Statistics?

An average in which different values contribute unequally based on their assigned weights.

Why is Weighted Average important?

Used in GPA calculation, financial analysis, polling, and any situation where data points differ in importance.

What do students usually get wrong about Weighted Average?

Weights don't have to be percentages — any positive numbers work as long as you divide by their sum.

What should I learn before Weighted Average?

Before studying Weighted Average, you should understand: mean fair share, stat expected value.

How Weighted Average Connects to Other Ideas

To understand weighted average, you should first be comfortable with mean fair share and stat expected value. Once you have a solid grasp of weighted average, you can move on to linear regression.