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Empirical and theoretical

The main distributions encountered at school are empirical distributions (created from data students collect) and theoretical distributions.

An example would be rolling a die many times and then comparing the results to a theoretical uniform distribution.

The figure below shows a comparison of 30 random tosses of a die and the theoretical uniform distribution of 5 of each outcome.


Two dot plots side by side. The first plot shows frequencies of 9, 6, 3, 7, 2 and 3 for each of the 6 outcomes; the second plot shows frequencies of 5 for each.

Empirical and theoretical results for die tosses.


Different graphical representations show different aspects of distribution. By being exposed to many graph types during the middle years, students are led to ask the question: "How are my data distributed?"

Students can be led to consider skewness, symmetry, overall spread, outliers, means, medians, clumps and gaps. 

Curriculum links

Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread