Expectation narrows the focus of data from its overall variation to a summary statistic, such as the arithmetic mean or most common value (mode), or to a theoretical value such as the probability of an event.
Questions arising from variation in data lead to investigations aimed at answering questions about expectation.
- What is the average daily maximum temperature in our city over a year?
- What is the most popular sport in this school?
- What is the probability of tossing a 4 on a normal die?
It is the relationship and contrast of expectation and variation that is at the heart of decision-making in statistics. For example, in comparing samples from two populations, are the differences between them meaningful? Research has shown that students often find decisions like these difficult to make.
Traditionally, measures of average have been introduced long before measures of variation. This has resulted in a focus on the expected representative measures without a suitable recognition of the variation that lies behind them.
There is further information on the fundamental ideas of expectation and variation in the article Inference as Prediction on the AAMT website.
