Comparative Numbers

There are certain numbers that help illustrate the performance of learners related to that of a whole class, or can express any irregularities in the average performance of a class.

Standard Deviation

The Standard Deviation shows the distance a quantity is likely to lie from its average value. In LearningSpace, it corresponds to a range where most of the results of a group of learners belong, in other words, how close the results of the learners are to each other.
This can help

• compare a learner's result to that of the whole class 
• and by extension, it can also provide a feedback about the applicability of the Cases.

If the standard deviation is either too big or too small, it could mean that something needs to be adjusted in the Activity management.

x = one particular kind of score of each learner of a learner group
m = mean performance of the learner group - calculated from the same kind of scores
n = number of learners in the learner group

You can calculate standard deviations for different groups of data, for example, for different levels of scores:

• item results,
• section results,
• Case results
• and Activity results.

Z-score

The Z-score always refers to the performance of a single learner: it reflects how much a specific learner's performance differs from the average. It is calculated from the learner score for a particular part of the Activity, a class average for the same scores and the standard deviation calculated from the preceding two numbers.

l = any kind of learner score
a = the class average calculated from the same kind of scores
d = the standard deviation calculated from the same scores and average

If this value is below -1 or exceeds +1, it means that the learner's section performance falls out of the class standard deviation, that is, they performed much worse or much better than the average in that section of the Activity. If the Z-score of a learner is near 0, it means that his section score is near the class average.

Percentile Score

The Percentile Score refers to a certain learner and shows how many percent of the class (more exactly the learner group) performed worse than (or the same as) the learner. 

n_w = number of learners whose particular performance was worse than or same as that of the learner
n = number of learners of the learner group of the Activity who have a record for the certain score

Percentile scores can be calculated for different kinds of scores, for example section results, Case results, Activity results. The percentile score is 100% for the best performing learner(s), while it is 0% for the weakest performing learners.