In order to be an informed citizen, employee and consumer, an adult needs to be able to reason statistically.
The amount of statistical information available to help people make decisions in business, politics, research and everyday life is vast. For example, consumer surveys guide the development and marketing of products, experiments evaluate the safety and efficacy of new medical treatments, and statistics sway public opinion on issues and represent (or misrepresent) the quality and effectiveness of commercial products.
Current thinking in statistics education emphasises the need for learners to undertake statistical investigations in order to understand statistics and use them wisely.
There are two main types of investigation. In the first type, learners pose questions, gather data and use the data to answer the questions. In the second type of investigation, learners look for patterns and trends in existing data sets and generate questions to be answered.
It is the second type of investigative approach that is addressed in these learning progressions. The decision to focus on existing data sets reflects the
fact that most adults are seldom engaged in data collection, but often need to consider data that has already been collected and presented.
Three of the four progressions in the Reason Statistically strand focus on different aspects of the investigative cycle: the Preparing Data for Analysis progression focuses on sorting and organising a given data set ready for analysis.
The Analysing Data for Interpretation progression uses statistical measures to describe the data set.
Finally, the Interpreting Data to Predict and Conclude progression supports the learner to make evidence-based statements about the data.
Probability learning progression
Probability impacts on people’s everyday decision making in such varied contexts as buying a lotto ticket, purchasing a car, taking medicine, or taking an umbrella to work (What are the chances of winning, surviving a crash in that particular model, experiencing one of the listed side effects, the forecasted rain eventuating?). Probability is often counter-intuitive in the way it operates, so it is important that people not assume that their initial assessment of a probability situation takes all the relevant factors into account and relates them correctly.
Because the impact of probability is so pervasive, it has given rise to a broad range of terminology, both informal and formal. Chance and likelihood are often used as synonyms for probability; probability may be expressed in terms of odds (particularly in gambling contexts), percentages and proportions.
The key ideas of probability that are developed in the learning progression are: Independent and dependent events: Where events are independent, the outcomes of past trials do not impact in any way on the outcomes of future trials. The probability of any event will be located somewhere on the impossible–certain continuum and can be expressed as a number between 0 and 1, a percentage between 0 and 100, or as odds (for example, 4:5, which is the same as 4/9).
The relative frequency with which a particular outcome occurs can be used as an estimate of its probability (known as experimental probability). The greater the number of trials or observations, the more accurate the estimate will be.
- In some situations, the precise probability of an event can be determined mathematically (known as theoretical probability).