Weighted Averages: When Some Values Count More

A plain average adds up the values and divides by how many there are — treating each one as equally important. But real situations often aren't equal: a final exam might count for 40% of your grade while a quiz counts for 5%, or a class of 30 students should count more than a class of 10 when you combine their averages. A weighted average accounts for those differences, and getting it right means avoiding the tempting mistake of simply averaging the averages.

This guide explains weighted averages and the trap to avoid, building on basic averages, with worked and practice problems matched to real test difficulty at Northside Tutoring.

Why Weighted Averages Matter

Weighted averages show up on the SAT, ACT, and SSAT in grade, mixture, and group-average problems — and in real life, from course grades to investment returns. They reward understanding what an average really represents, not just plugging into a formula.

The Core Idea

In a weighted average, each value carries a weight reflecting how much it counts. A value with a big weight pulls the average toward itself more than a value with a small weight. A regular average is just the special case where every weight is equal.

The Formula

Multiply each value by its weight, sum those products, and divide by the total weight:

Example: Grades

Suppose tests are 60% of your grade and homework is 40%. With a test average of 90 and a homework average of 80:

The result, 86, leans toward the tests because they carry more weight — not the simple average of 90 and 80 (which would be 85).

Combining Group Averages

To combine the averages of different-sized groups, weight each average by its group size. If a class of 20 averages 75 and a class of 30 averages 85, the combined average is the total of all points divided by the total students: (20·75 + 30·85)/(20 + 30) = (1500 + 2550)/50 = 4050/50 = 81.

The Average-of-Averages Trap

This trap appears constantly. The moment a problem combines groups of different sizes (or values of different weights), reach for the weighted average, not the plain one.

Where You'll See This — Test by Test

Weighted averages are tested on the SAT, ACT, and SSAT in grade, mixture, and group-average problems. The key is recognizing when values carry different weights and avoiding the average-of-averages trap.

Watch the Lesson

Sometimes a diagram needs a voice. In the short video below, one of our Northside tutors walks through the core idea and works through test-style problems in real time.

Worked Example Problems

These problems are calibrated to the difficulty you'll actually see on test day. Try each one before opening the solution.

Common Mistakes to Avoid

Practice Problems — You Try

Three problems below. Work each before checking the solution.

The Northside Method — How We Teach This 1-on-1

Reading a blog is a great starting point. But there's a meaningful gap between understanding a concept and reflexively applying it under timed conditions. That gap is exactly what our tutors close.

Every Northside student works through a four-step framework:

1. Assessment. We diagnose which specific skills are slowing your student down — not just whether they "get it" in the abstract.
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