M7L2: Measures of Variance

Measures of Dispersion

Tools that tell us how spread out or scattered class scores are, complementing central tendency.

Range (R)

The simplest measure of variability, calculated by subtracting the lowest score from the highest score (H - L).

Range Limitation

An unstable metric in public schools because extreme outliers (like a top scholar vs. a struggling student) can heavily exaggerate class variability.

Variance and Standard Deviation (SD)

Metrics that use every single score in the distribution to figure out the average distance or error of scores from the mean.

Low Standard Deviation

A tight clustering of scores around the mean, creating a tall, narrow, and peaked curve (Leptokurtic).

Homogeneous Class

A group of students with very similar abilities where a low SD makes whole-group teaching work really well.

High Standard Deviation

Scores that are spread far apart, creating a flat and wide curve (Platykurtic) with a big achievement gap.

Heterogeneous Class

A diverse group of students with a high SD, requiring the teacher to use Differentiated Instruction and peer tutoring.

SD for Total Class Scores

When looking at overall test totals, we want a low SD because it shows universal mastery across the board.

SD for an Individual Test Item

For single test questions, we need variance; an item with zero SD fails to separate top students from low achievers.