Statistics: centre, spread and distributions

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

• Adult beginner pathway

Further reading

• David Freedman, Robert Pisani and Roger Purves, Statistics