Variability

Variability shows how scores vary in a distribution. There are several ways of estimating the variability of scores, but as a language teacher you need to know only two of them: range and standard deviation.

Range
It simply means the difference between the highest score and the lowest score. In the formula, you have to add 1 because you have to take into account the upper limit of the highest score (0.5) and the lower limit of the lowest score (0.5).

Range = H - L + 1

Standard deviation
Standard deviation shows how far a particular score deviates (moves away) from the mean. You can compute standard deviation by using the following formula:


The smaller the standard deviation, the more homogeneous the group of scores is. The larger the standard deviation, the more heterogeneous it is.