- 21 Jun 2022
- 6 minutes to read

# Grade aggregation methods

- Updated on 21 Jun 2022
- 6 minutes to read

Activities within a course can be assigned a mark and each of these marks can be aggregated using a variety of methods to give a total grade for the course or a grade category. When setting up or editing a course you can change the aggregation method used.

Method | Description | Example |
---|---|---|

Natural (default) | The sum of all grade values scaled by weight. | As an example we can say a learner has received the following grades: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
If you do not force grade weights we end up with the calculation: (70 + 20 + 10)/(100 + 80 + 10) Here we are adding together the grades received for each assignment first: 70 + 20 + 10 = 100 Then we are adding up all of the maximum grades for each assignment: 100 + 80 +10 = 190 If we then represent this as a fraction we have 100/190 (52.6%) as the final aggregated grade. |

Mean of grades | The sum of all the learner's grades for that divided by the total number of grades (this also means items that can be graded). | Let's imagine a learner scored the following: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
The category max grade is 100 and it uses the The grade is calculated as: (0.7 + 0.25 + 1.0)/3 = 0.65 This is because the calculation is done in percentages with 100% represented as a whole number (1.0) and lower percentages represented as a fraction (e.g 0.7 for 70%). So we add all the grades together: 0.7 + 0.25 + 1.0 = 1.95 Then we divide this by the total number of grades, in this case there are 3 grades, so we divide by that (note that the / represents a division symbol). 1.95 ÷ 3 = 0.65 After converting that fraction back into a percentage, the users total aggregated grade is 65/100 (65%). |

Weighted mean | Grades can be given weighting to distinguish how important they are, for example assignment 1 might be less important that assignment 3 and therefore assignment 3 might be given a higher weighting. Totara Learn will calculate the category total by taking each grade and multiplying it by it's weighting, adding all the weighting together and then dividing the sum of all multiplied grades by the sum of all weightings. | For example, consider the following scenario: A learner has received the following grades: - Assignment 1: 70/100 (70%). Item weight: 10
- Assignment 2: 20/80 (25%). Item weight: 5
- Assignment 3: 10/10 (100%). Item weight: 3
The category max grade is 100 and the The grade is calculated as: (0.7*10 + 0.25*5 + 1.0*3)/(10 + 5 + 3) = 0.625 We can break this down. First. the grades are calculated as a percentage and then multiplied by their weighting (the asterisk acts as a multiplication symbol). So we get: 0.7 x 10 =7 0.25 x 5 =1.25 1.0 x 3 =3 Then we add those all together to get 11.25 (this replaces the sum in our first set of brackets). We then have to add all the weights together, so in this case 10 + 5 + 3 = 18 (this replaces the sum in our second bracket). S Now we are dealing with the first calculation divided by the second (the / in the original equation symbolises a division symbol). That gives us 11.25 ÷ 18 = 0.625 As we are dealing with percentages 0.625 gives us 62.5% (62.5/100) as the final aggregated grade. |

Simple weighted mean | This method is similar to the weighted mean of grades, but instead uses each grade item's maximum possible grade as the weighting. | We can break down how this works by looking at an example. A learner has received the following grades: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
The category max total grade is 100 and it is using the The calculation goes as follows: (0.7*100 + 0.25*80 + 1.0*10)/(100 + 80 + 10) = 0.526 First we take each grade and multiply it by that items maximum possible grade, giving us: 0.7 x 100 = 70 0.25 x 80 = 20 1.0 x 10 = 10 If we add all of those together we get 100 (this replaces the equation in the first set of brackets). Next we add up all of the maximum possible grades, 100 + 80 +10 = 190 (this replaces the equation in the second set of brackets). Now we have to divide the first sum by the second (the / symbolises a division symbol), giving us 100 ÷ 190 = 0.526. When we convert this back into a percentage (out of the category maximum 100) we are left with 52.6% (52.6/100). |

Median of grades | The middle grade when grades are arranged in order of size. | If we imagine that a learner achieved the following grades: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
We can calculate the total grade for category with a max grade of 100 that is using the We then simply take the middle number (the median) and that is the final grade, so 70/100 (70%). |

Smallest grade | This takes the smallest grade and uses that as the overall category total. | For example, if a learner scored the the following: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
The category total is calculated out of 100 and the aggregation method is The smallest grade is 25% therefore the aggregated grade for the category would be 25/100 (25%). |

Highest grade | The takes the highest grade and uses that as the overall category total. | For example, if a learner scored the the following: - Assignment 1: 70/100 (70%)
- Assignment 2: 20/80 (25%)
- Assignment 3: 10/10 (100%)
The category total is calculated out of 100 and the aggregation method is The highest grade is 100% therefore the aggregated grade for the category would be 100/100 (100%). |

Mode of grades | The grade that occurs the most frequently. This is most useful to use with non-numerical grades (such as A,B,C,D) as there is likely to be more consistency in the numbers occurring because behind each letter grade is a number (e.g A=100, B=80, C=60). | We can take the example of a learner who has scored the following: - Assignment 1: 70/100 (70%)
- Assignment 2: 35/50 (70%)
- Assignment 3: 20/80 (25%)
- Assignment 4: 10/10 (100%)
- Assignment 5: 7/10 (70%)
The category max grade is 100 and the aggregation method is We then look at the grades as a percentage and see which occurs most frequently, in this case it is 70% so the final category total would be 70/100. |

## Old methods

### Mean of grades (with extra credits)

This is now unsupported but still available to allow backward compatibility with old activities.

An extra credit value greater than 0 changes the grade aggregation calculation. The extra credit number is multiplied by the grade and added to the sum of all grades, but the extra credit value is not included in the division. For example:

- Item 1 is graded 0-100 and its
**Extra credit**value is set to 2 - Item 2 is graded 0-100 and its
**Extra credit**value is left at 0.0000 - Item 3 is graded 0-100 and its
**Extra credit**value is left at 0.0000 - All 3 items belong to Category 1, which has
**Mean of grades (with extra credits)**as its aggregation strategy - A learner gets graded 20 on Item 1, 40 on Item 2 and 60 on Item 3
- The learner's total for Category 1 will be 90/100 since 20*2 + (40 + 60)/2 = 90

The Totara Academy has a whole course dedicated to using Grading, completion, and certificates in Totara Learn. Here you can learn more on how to use these tools, see best practice, and give it a go yourself.

© Copyright 2024 Totara Learning Solutions. All rights reserved. Some content originally obtained via GPLv3 license and continues to be available under GPLv3. All other content is the sole copyright of Totara Learning Solutions.