Updates to Overall Rubric Mean and Standard Deviation Calculations in Rubric Reports
With this release, the overall mean and overall standard deviation values for a rubric in the rubric report are calculated based on the mean scores for individual elements in the rubric.
NOTE: Previously, the overall mean and overall standard deviation values for a rubric in the rubric report were calculated based on the total rubric score received by the assessees on the rubric.
So if a rubric has 10 elements and the rubric report has a single query, with the report output showing the following mean score values for individual elements of the rubric:
| Element | Mean |
|---|---|
| Element 1 | 4 |
| Element 2 | 3 |
| Element 3 | 4 |
| Element 4 | 2 |
| Element 5 | 4 |
| Element 6 | 3 |
| Element 7 | 3 |
| Element 8 | 3 |
| Element 9 | 4 |
| Element 10 | 2 |
OVERALL MEAN CALCULATION:
Now, the formula used to calculate the overall mean will be Σ(xi) ∕ n, where:
- xi = each element’s mean
- n = number of filtered elements
- Σ = sum of all values
So, as per the example, the overall element mean would be [(4 + 3 + 4 + 2 + 4 + 3 + 3 + 3 + 4 + 2) ∕ 10]= 3.2
OVERALL STANDARD DEVIATION:
Now, the formula used to calculate the overall standard deviation will be σ = √
{Σ(xi − μ)² ∕ (n − 1)}
, where:
- σ = standard deviation
- xi = each element’s mean
- μ = overall mean
- n = number of filtered elements
- Σ = sum of all values
So, as per the example, the calculation for the standard deviation would be:
= √
{[(4 − 3.2)² + (3 − 3.2)² + (4 − 3.2)² + (2 − 3.2)² + (4 − 3.2)² + (3 − 3.2)² + (3 − 3.2)² + (3 − 3.2)² + (4 − 3.2)² + (2 − 3.2)²] ∕ (10−1)}
= √
{[0.64 + 0.04 + 0.64 + 1.44 + 0.64 + 0.04 + 0.04 + 0.04 + 0.64 + 1.44] ∕ 9}
= √
{5.6/9}
= √
{0.62222222}
= 0.79
IMPORTANT NOTE: If the report output is further filtered to display results for only a select few elements, the Overall Mean and the Overall Standard Deviation values would also be calculated based on just the selected elements.
User Demographics: Additional option available for the Race\Ethnicity
With this release, administrators will be able to import an additional value (i.e. "Middle Eastern or North African") for Race\Ethnicity as part of the user import.