Mathematics — first biennium · Lesson
A measure is useful only when it answers the right question. The mean is sensitive to extreme values; the median is more robust. Spread should be read together with the representation and numerical measures.
Prerequisites: Measures of centre and spread
Goal: Critically choose measures of centre and spread in the presence of extreme values and compare the graph with the numbers.
In this lesson: Critically choose measures of centre and spread in the presence of extreme values and compare the graph with the numbers.
New concept: One measure is not enough to compare distributions: centre and spread answer different questions. An outlier is a value far from the others and can strongly increase range, variance and standard deviation.
How to proceed: Do not choose the mean automatically. First look for values far from the rest and compare the graph with the numerical measures.
You can already assume: Measures of centre and spread.
A: A — regular distribution · B: B — with an extreme value
The dot plot preserves every observation: B's extreme value is immediately visible and explains why mean and range react more than the median.
Completed exercises: 0/5 · Correct on first attempt: 0
Do not choose the mean automatically. First look for values far from the rest and compare the graph with the numerical measures.
Data / situation: A: 8, 9, 10, 11, 12. B: 8, 9, 10, 11, 18.
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.