Scoring with Weights and Randomization

Let us take an example where questions are organized into groups with weights and randomization. The test creator has created two groups of questions: Pronunciation group and Fluency group with weights of 70% and 30% respectively.

The score for such an assessment is calculated as a weighted average of the individual question scores, using the following formula:

Score = Sum of (Question score x Weight of Question)/100

Since two questions are randomly selected from the Pronunciation group (70% weight), each will carry a weight of 35% (70/2). The one randomly selected question from the Fluency group will have weight of 30%.

As an example, if the Speechace scores for the two Pronunciation questions are 8.9 and 8.6, and the one Fluency question is 8.6 (all out of 9.0), the final assessment score will be 8.7 out of 9.0 as per the calculation below:

$$[(8.9*35)+(8.6*35)+(8.6*30)]/100=8.7$$