Statistics and probability strand

Students should be able to:

SP.1

Outcomes of experiments

Listing and organising outcomes

  • generate a sample space for an experiment in a systematic way, including the use of tree diagrams for successive events and two-way tables for independent events.
  • use the fundamental principle of counting to solve authentic problems.
SP.2

Random events and probability

Understanding probability

  • demonstrate understanding that probability is a measure on a scale of 0–1 of how likely an event (including an everyday event) is to occur.

Equally likely outcomes

  • use the principle that, in the case of equally likely outcomes, the probability of an event is given by:
    number of outcomes of interest ÷ total number of outcomes.

Relative frequency

  • use relative frequency as an estimate of the probability of an event, given experimental data, and recognise that increasing the number of times an experiment is repeated generally leads to progressively better estimates of its theoretical probability.
SP.3

Statistical investigations

Statistical questions

  • generate a statistical question.

Data collection

  • plan and implement a method to generate and/or source unbiased, representative data, and present this data in a frequency table.
  • classify data (categorical, numerical).

Graphical representations

  • select, draw and interpret appropriate graphical displays of univariate data, including pie charts, bar charts, line plots, histograms (equal intervals), ordered stem-and-leaf plots, and ordered back-to-back stem-and-leaf plots.

Summary statistics

  • select, calculate and interpret appropriate summary statistics to describe aspects of univariate data.
    Central tendency: mean (including of a grouped frequency distribution), median, mode.
    Variability: range.

Evaluating displays

  • evaluate the effectiveness of different graphical displays in representing data.

Misconceptions and misuse

  • discuss misconceptions and misuses of statistics.

Limitations and interpretation

  • discuss the assumptions and limitations of conclusions drawn from sample data or graphical/numerical summaries of data.