# Natural Weighting

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At a basic level, natural weighting functions as sum of grades.  In addition, however, users can configure natural weighting to take advantage of additional features, such as weighting grades.  Natural weighting can produce either a sum or a mean, with or without weights, depending on instructor needs.  As such, natural weighting serves as a single aggregation method that can supersede sum of grades, mean of grades (with or without extra credit), and both weighted mean and simple weighted mean of grades.

### Natural Weighting as a sum of grades

By default, natural weighting produces a sum of the grades. In the example below, there are three grade items worth 100, 50, and 20 points (for a total of 170 possible points). Using natural weighting, Moodle adds up a student’s scores on the three items and reports the total (the sum). The Weights column displays the relative weights of the items (as percentages) based on each item’s points. For example, since 100/170 = 0.588235…, the Weights column for the 100-point item displays a percentage of 58.824. If the weights are not overridden by selecting them, then they are simply for informational purposes, to inform the instructor what the relative weights of the items are.

### Natural Weighting as a sum of grades with custom weights

Compare this method to the old Simple Weighted Mean aggregation method. Instructors can override grade items’ default weights and enter alternate weights instead, by checking the box next to any of the weights. In the example below, the 20-point item (Grade Item 3) is actually worth half of the total grade, so the instructor checks its box in the Weights column and enters a value of 50%, overriding the default weight with the desired value. When the instructor overrides any of the default weights, the other weights in the category automatically adjust to compensate, so that the total of all the items remains 100%. When Grade Item 3 is adjusted to be worth 50%, the other two items’ weights adjust to 33.333% and 16.667% percent, respectively, based on the number of points in each item. The 100-point item is still worth twice as much as the 50-point item, so this is reflected in the weights. The same scores from the previous example (50 out of 100, 40 out of 50, and 18 out of 20) would now be calculated like this:

= ((((50/100)*33.333) + ((40/50)*16.667) + ((18/20)*50))/100)*170
= (((0.5*33.333) + (0.8*16.667) + (0.9*50))/100)*170
= ((16.667 + 13.334 + 45)/100)*170
= (75.001/100)*170
= 0.750*170
= 127.5

Displayed as a percentage, this would be 127.5/170 = 75%.

Whenever weights are applied to scores, the scores are first normalized before the weights are applied. Normalization means that the raw score is converted into a ratio between 0.0 and 1.0. For example, a score of “18 out of 20” is normalized as 18/20 = 0.9, while a score of “50 out of 100” is normalized as 50/100 = 0.5. This means that “18 out of 20” is a higher score than “50 out of 100” even though the raw score of 50 is higher numerically than the raw score of 18.

### Natural Weighting as a sum of grades, plus extra credit

This is a new capability: previously you could not assign extra credit in a sum of grades. A grade item can act as extra credit for the category. This means that the grade item’s maximum grade will not be added to the category total’s maximum grade, but the item’s grade will. An example:

• Item 1 is graded 0-100

• Item 2 is graded 0-75

• Item 1 has the “Act as extra credit” checkbox ticked, Item 2 doesn’t.

• Both items belong to Category 1.

• Category 1’s total will be graded 0-75

• A student gets graded 20 on Item 1 and 70 on Item 2

• The student’s total for Category 1 will be 75/75 (20+70 = 90 but Item 1 only acts as extra credit, so it brings the total to its maximum)

*Note that this is not a solution for providing extra credit within a grade item, say, for an extra credit question on an automatically graded quiz, but for adding extra credit as a separate grade item.

### Natural Weighting as a mean of grades without extra credit

To have natural weighting function as a mean of grades, the instructor can override the weights so that they are all equal, for example, by setting all of the weights to a value of 1. When the changes are applied with the Save Changes button, Moodle converts the numbers into the appropriate percentages.

### Natural Weighting as a mean of grades with extra credit

To have natural weighting function as a mean of grades with extra credit, an instructor can proceed as above for mean of grades, but also check “act as extra credit” on one or more items, so that they cease to contribute to the total from which the mean is calculated, but add to the total points accrued by a student in the category where the extra credit grade item has been placed.