Mathematics — first biennium · Lesson
The range uses only the minimum and maximum. Variance and standard deviation use every deviation from the mean and describe how far data spread around the centre.
Prerequisites: Comparing distributions
Goal: Calculate deviations, variance and standard deviation and interpret them as measures of spread around the mean.
In this lesson: Calculate deviations, variance and standard deviation and interpret them as measures of spread around the mean.
New concept: Variance is the mean of the squared deviations from the mean; standard deviation is the square root of variance and returns to the original data unit. Larger values generally indicate greater spread.
How to proceed: Here every deviation from the mean has absolute value 4: squaring gives 16 each time. Standard deviation returns to the original unit by taking the square root of the variance.
You can already assume: Comparing distributions.
A: Exercise dataset · B: Less spread comparison
The two datasets have the same centre, but the exercise dataset is more spread out: the dot plot makes variance and standard deviation visible.
Completed exercises: 0/5 · Correct on first attempt: 0
Here every deviation from the mean has absolute value 4: squaring gives 16 each time. Standard deviation returns to the original unit by taking the square root of the variance.
Data / situation: Data: 4, 4, 12, 12.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.