Using category averages takes into account the category factors.

For example:

Categories and factors:
Quiz 1
Homework 1
Tests 2


Assignments:

Quiz 1: 9 out of 10 9/10 = 90%
Quiz 2: 6 out of 10 6/10 = 60% Category average = 73.3
Quiz 3: 7 out of 10 7/10 = 70%

Homework 1: 10 out of 10 10/10 = 100%
Homework 2: 9 out of 10 9/10 = 90 % Category average = 96.6
Homework 3: 10 out of 10 20/10 = 100%

Test 1: 90 out of 100 90/100 = 90% Category average = 82.5
Test 2: 75 out of 100 75/100= 75%

Using assignment averages: Calculates using the sum of grades divided by the number of grades

= (73.3 + 96.6 + 82.5) / 3 = 84.1

Using category averages: Sum of (Category average * Category factor)/ Sum of factors

(73.3 * 1) + (96.6 * 1) + (82.5 * 2) / 4 = 83.75

Calculating using category averages takes into account the factors assigned to each category.