Calculations
Calculation overview
The calculations in the Edit|Calculation command have names that represent the type of mathematical operation they perform. This means that for some of the calculations you may want to do, the relevant calculation type may not obvious at first.
For example, the Linear Scale calculation can convert the results in one task to be out of a different maximum by multiplying each result by the appropriate number. This means this calculation type can be used to convert a set of results to a percentage by doing a linear to a task maximum of 100.
Here is a summary of the more commonly used calculation types. For more information refer to the Calculation types topic in the Calculations section.
| Calculation Type | Description |
| Average | Adds the results in separate tasks, but first converts each result to a percentage before adding to make the total for each student. |
| Combine | Adds the results in separate tasks to make a single total for each student. |
| Grade | Assigns alphabetical or numerical grades based in the results in a single task. |
| Linear Scale | Multiplies a single task by factor to change the maximum of the task and all the results. |
| Moderate | Assigns the results of one task to the students based on the results in another task. |
| Standardise | Changes the distribution of the results in a single task so the task has a specified mean and standard deviation. |
| Rank | Assigns positions to students based on the results in a single task. |
| Weight | Adds tasks like the Average command and lets you specify a weighting for each task; can optionally standardise each task before adding. |
Average
The Average calculation converts each result to a percentage before adding the tasks together. The default task maximum is equal to 100.
Since the results are initially converted to a percentage each task contributes equally to the final total. This means the Average command gives different results from the Combine command if each task has a different maximum.
For example, if two tasks are averaged and one task has a task maximum of 20 and the other a maximum of 100, the task with a maximum of 20 will first be multiplied by 5 to make it out of 100. The two results are then added. After the addition, the total is divided by 2 to bring the total back to a percentage.
The effect of the Average command is the same as the Weight command with each task being given a weight of 1 and there being no standardisation.
Combine
The Combine calculation adds the results of selected tasks using a simple mathematical sum. When storing the results of the combined tasks, the default task maximum is the sum of the maximum of each task selected for the combine.
Grade
The Grade calculation assigns a grade to each student based on the results in a task. The grades are initially A to E although they can be changed to up to thirty different grades with the Preferences command.
There are three different grade calculations that let you specify the number of each grade to give.
- Grade with set number
- Grade with percentages
- Grade with cut-off
| Grade Type | Description |
| Grade with set number | This lets you specify the exact number of each type of grade to give. For example, the top 10 students may be given A, the next 20 a B and so on. |
| Grade with percentages | This lets you specify what percentage of students gets each grade. For example, the top 20% are given A, the next 50% a B, and so on. If there are 30 students, then 6 students would get an A, because 6 is 20% of 30. |
| Grade with cut-off | This lets you specify the lowest result that each grade can be given to. For example, give an A to all results from 80 to 100, a B to all results from 40 to 80, and a C to all results from 0 to 40. This means any student with a result greater than or equal to 80 gets an A. The rest of the students with results greater than or equal to 40 get a B and so on. |
When assigning grades by set number or percentage it is possible that the correct number of a particular grade has been assigned, but the next student has the same result. In this case, SM-Marks Online always gives equal grades to equal results.
This may mean that if you want to give out 10 grades but there is more than one student in the tenth position with the same result, then more than 10 grades will be given.
Linear Scale
The Linear Scale calculation multiplies a task by a factor to change the task maximum and all the results in the task. You do not specify the factor required; instead the new task maximum must be given. SM-Marks Online calculates the required factor and uses it internally.
Moderate
The Moderate calculation gets the results from one task and gives those results to the students based on the results in a second task.
This means the student with the top result in a task is assigned the top result in another task. The second student gets the second result and so on, down to the last student.
Rank
The Rank calculation gives positions to students based on the results in a task. The first student gets a position of 1, the second a position of 2, and so on.
When assigning ranks you can specify the number of figures after the decimal point considered significant.
If two or more students have the same result after rounding, the command gives the students that same position with an equals sign next to the number. The next position is then skipped.
If you do not want to assign equal positions set the task with the results being ranked to show one or more decimal places, with the Edit|Decimal places command. If two students still have exactly the same result, the position is decided by the name of the student. The student with a name closest to the beginning of the alphabet gets the higher position.
Weight
The Weight calculation converts each task to a percentage and then multiples it by a weighting factor before adding the tasks to get the final result for each student. The task can also be standardised to a specified mean and standard deviation instead of converting it to a percentage if required.
The weighting given to each task can be either a decimal or a whole number, or a combination of both.
For example, three tasks are to be weighted to make a new total with weights of 10%, 30%, and 60%. The weights specified in the Weight command could be 0.1, 0.3, and 0.6. Weights of 10, 30, and 60 give exactly the same results. So would 2, 6, and 12.
It is the ratio of the weights that determines the contribution each task makes to the final result, not the actual numbers used.
Sometimes it is necessary to make sure each task has the same mean and standard deviation before adding the tasks. In this case, you should specify the required mean and standard deviation with the Weight command.