A summary is a single number that stands for a whole data set, and each summary tells a different part of the story. This cluster teaches you to choose the one that fits the question, and to explain why.
It extends dispersion of ungrouped data in SPM Mathematics.
What do the four pages cover?
- Comparing two classes with equal means but different spread: why the mean alone is not enough.
- Explaining how an outlier changes the mean and median differently: which measure resists an extreme value.
- Reconstructing a missing observation from a mean and checking plausibility: using the mean backwards and testing the answer.
- Deciding whether two data summaries are genuinely comparable: when a comparison is unfair.
A practice set closes the cluster.
One data set, two stories
Five pupils save RM10, RM12, RM13, RM15 and RM100 in a month. The mean is 150 ÷ 5 = RM30. The median is RM13.
The mean says a typical pupil saves RM30, yet four of the five saved less than RM16. The median tells the truer story of a typical pupil, because the RM100 pulls the mean upward. The choice of summary changed the message.
Who should start where?
A student who can calculate every measure but loses marks on wording should begin at the first page. A student preparing for questions that say “explain” or “justify” can go straight to the outlier and comparability pages.
Use the descriptive statistics explorer to test your predictions on invented data. For a teacher to question your reasoning, see online one-to-one Mathematics tuition.