Quiz statistics calculations in practice

Here I'm going to document what the code actually does. Documenting it here principally because I can't use TEX notation in php comments, well I guess I can but only real TEX geeks will be able to read it :-)

Notation used in the calculations

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Calculating MEAN of grades for all attempts by students

$$\displaystyle = \bar{T} = \frac{1}{S} \sum_{s \in S} T_s$$

We calculate the MEAN of first and all attempts by :

• fetching two totals and counts of all grades for attempts from the db the total grades for first attempts and the rest of the attempts.
• then to get the mean of first attempts :
  • we divide the total grade for all first attempts.
• for the mean for all attempts :
  • we add the total of all first attempts to the total for the rest of the attempts (not the first attempt) and divide by the total count of first attempts plus the total count of the rest of the attempts.

Depending on whether we are calculating the rest of the statistics for all attempts or for just the first attempts we select the appropriate mean to use in the rest of the calculations and save a empty string or a string of sql that selects first attempts only.