Grades 6–8Probability & StatisticsPlanned
Statistics: centre, spread and distributions
Statistical questions, distributions of data, measures of centre (mean, median, mode) and spread (range, interquartile range), box plots and histograms.
math.prob.statistics-intro
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 9
You will learn to
- Distinguish statistical questions, which anticipate variability, from non-statistical ones.
- Compute mean, median, mode, range and interquartile range, and choose an appropriate summary.
- Draw and compare histograms and box plots of two data sets.
Definition
- The median is the middle value of an ordered list, or the mean of the two middle values.
- The range is the largest value minus the smallest; the interquartile range is Q₃ − Q₁.
- An outlier is a value far from the rest of the data.
Theorem
- The median is resistant to outliers; the mean is not.
- Two data sets can have the same mean but very different spreads.
Common misconceptions
- Thinking the mean is always the best summary of centre.
- Comparing two groups by their centres alone and ignoring spread.
Leads to
Optional discoveries
- Statistical inference Formal statistics models data as random samples and quantifies uncertainty with confidence intervals and tests.
- ← Data, tallies and picture graphs
Learning pathways
Further reading
- David Freedman, Robert Pisani and Roger Purves, Statistics