Certain numbers help illustrate the performance of learners relative to that of a whole class or express any irregularities in the average performance of a class.

Standard Deviation

The Standard Deviation indicates how far a quantity is likely to deviate from its average value. In LearningSpace, it corresponds to a range where most of a group of learners' results belong, in other words, how close the learners' results are to each other.

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 in 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 outside the class standard deviation. They performed much better or worse than average in that section of the Activity. If a learner's Z-score is near 0, it means his section score is near the class average.

Percentile Score

The Percentile Score refers to a specific learner and indicates what percentage of the class (more precisely, the learner group) performed worse than (or the same as) that learner.

The Percentile Score is always a percentage: the number of learners whose performance was worse than or equal to that of the learner whose percentile score is being calculated, divided by the number of learners in the Activity's learner group with a record of that score.

nw = number of learners whose particular performance was worse than or the 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 scores, such as section, Case, and Activity results. The percentile score is 100% for the best-performing learner(s), while 0% for the weakest one.