Weighted average facts for kids

A weighted average is a special kind of average where some numbers are more important than others. Imagine you have different groups of things, and each group has a different size or "weight." A weighted average helps you find the true average by considering how big or important each group is. You find it by multiplying each value by its importance (its "weight"), adding all those results together, and then dividing by the total importance (the sum of all the weights).

Understanding Weighted Averages with an Example

Let's look at two school classes and their test grades.

• Morning class: 20 students
• Afternoon class: 30 students

The grades for the morning class were: 62, 67, 71, 74, 76, 77, 78, 79, 79, 80, 80, 81, 81, 82, 83, 84, 86, 89, 93, 98. The average grade for the morning class is 80.

The grades for the afternoon class were: 81, 82, 83, 84, 85, 86, 87, 87, 88, 88, 89, 89, 89, 90, 90, 90, 90, 91, 91, 91, 92, 92, 93, 93, 94, 95, 96, 97, 98, 99. The average grade for the afternoon class is 90.

If you just average the two class averages (80 and 90), you get 85. But this isn't the true average grade for all students combined! Why? Because the classes have different numbers of students. The afternoon class has more students, so its grades should count more towards the overall average.

Calculating the True Average Grade

To find the actual average grade for all students, you can add up every single grade from both classes and then divide by the total number of students (20 + 30 = 50).

So, the real average grade for all students is 86.

Using Weights for a Faster Calculation

You can also find this overall average using a weighted average of the class averages. Here, the "weights" are the number of students in each class.

• Morning class average: 80 (weight: 20 students)
• Afternoon class average: 90 (weight: 30 students)

The formula for the weighted average is:

This calculation gives us the same correct average of 86. The weighted average is very useful when you only know the average of each group and the size (or weight) of each group, but not every single individual value.

See also

In Spanish: Media ponderada para niños