Weighted Mean Explained Simply (With a Real-Life Example)
- Tyler Buffone
- Jan 14
- 2 min read
Understanding averages is a key skill in high school math, but not all averages are created equal. In many real-life situations, some values matter more than others. This is where the weighted mean comes in.
As a Winnipeg tutor, I regularly see students struggle with this concept, not because it’s difficult, but because it’s often explained too abstractly. Let’s break it down in a clear, practical way.
What Is a Weighted Mean?
A weighted mean is a type of average where some values count more than others.
This happens when:
One value appears more frequently than another, or
One value represents a larger quantity or amount
Instead of treating every number equally, we assign a weight to each value. The weight tells us how important that value is.
In many word problems, the weight is something tangible, like:
Number of items
Number of hours
Number of gallons
The Weighted Mean Formula
Here is a very simple version of the weighted mean formula:
How to think about it
Value = the number you are averaging
Weight = how much of that value there is
In everyday terms:
Multiply each value by how much of it you have, add everything up, then divide by the total amount.
Why Weighted Means Matter in Real Life
Weighted means show up everywhere:
Calculating average test grades when assignments are worth different percentages
Finding average speed over trips of different distances
Calculating average prices when you buy different amounts at different prices
A very common example for students is gas prices, so let’s look at one.
Example: Average Gas Price Using a Weighted Mean
Maya bought gas for her car four times during one month:
12 gallons at $1.95 per gallon
9 gallons at $2.05 per gallon
14 gallons at $2.00 per gallon
10 gallons at $2.10 per gallon
Question: What was the average price per gallon she paid?
Step-by-Step Solution
Step 1: Find the cost of each purchase
Multiply gallons (weight) by price (value).
12 × 1.95 = 23.40
9 × 2.05 = 18.45
14 × 2.00 = 28.00
10 × 2.10 = 21.00
Step 2: Add the total cost
23.40 + 18.45 + 28.00 + 21.00 = 90.85
Total amount spent: $90.85
Step 3: Add the total number of gallons
12 + 9 + 14 + 10 = 45
Total gallons purchased: 45
Step 4: Divide total cost by total gallons
Average price = 90.85 / 45 = 2.018888...
Rounded to the nearest cent: $2.02 per gallon
Quick Reasonableness Check
All gas prices were between $1.95 and $2.10, so the average must also fall between those values. Since $2.02 is in that range, the answer makes sense.
Final Takeaway
A weighted mean is just an average that respects quantity. Whenever amounts are unequal, a regular average won’t give the right answer. Learning to recognize these situations is a skill that pays off in math class and beyond.
Need help with weighted mean? If you’re in Winnipeg and looking for a tutor, Tutor Advance provides expert one-on-one support!