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Aug 16

## The pearls of AP Statistics 9

Your word is gold. Don't be sloppy with definitions and their sequencing: they are the foundation of theory.

They say: Do the data have a single mound? A distribution of such data is called unimodal. The highest point is at the mode. A distribution with two distinct mounds is called bimodal. (Agresti and Franklin,p.39)

I say: Is this supposed to be the definition of the mode? The mode is not defined explicitly, whereas the notions of a unimodal and bimodal distributions derive from it. Later, on p. 57, the mode is said to be the most frequent value; this should have been said in the beginning.

One of the biggest drawbacks of AP Statistics is absence of logical order. Show your students what comes from where.

A definition starts with a preamble which sets a background and allows you to see the existence of objects with distinct properties. Most of the time the preamble is not even mentioned but there are cases when it contains a complex logical argument. After you understand the preamble understanding the definition proper – that is giving the name – becomes easy. Studying a definition is concluded by considering possible equivalent definitions and deriving immediate consequences.