# GMC6: Understanding data and risk

This list contains a collection of resources to help meet General Mathematical Competency 6 (GMC6). More resources to support T level Science can be found on our T Level science resource packages page.

**GMC6 states:**

Students should:

- make data clear and presentable
- make sure data is accurate
- use of software to produce collection of measurements and images, including diagrams, graphs and charts, that best communicate information to intended audiences and reflect ‘clinical standard’ practice
- understand that graphical data may require the identification and validation of mathematical functions to appropriately model the data
- demonstrate an understanding of how data is generated, sifted, selected, sampled and organised
- understand that separation techniques for data processing procedures and outputs should be interrogated and interpreted critically against principle knowledge

Students should be aware of, and be able to communicate risk in a variety of situations for example

- explaining risks to patients if asked
- advising individuals and families about risks of genetic disorders
- account for the effects, implications, risks and issues associated with recording patient information

### Evaluating Probability Statements S2

In this resource, students discuss and clarify some common misconceptions about probability. This involves discussing the concepts of equally likely events, randomness and sample sizes. They will also learn to reason and explain. This session assumes that learners have encountered probability before. It aims to draw on their prior knowledge and develop it through discussion, it does not assume that they are already competent.

### Spread of disease

This resource enables students to explore various models of the spread of disease.

The presentation has links to instructions for three activities:

- a practical investigation using a die and counters to model the spread and decline of a disease and an activity sheet to record these results.
- a document which shows how a pack of playing cards can be used to model the spread of disease in a population.
- an Excel file which shows how a population can be affected by a disease. Various factors such as incubation period can be altered on the spreadsheet and the graphs show the effect of those changes. The presentation includes a series of questions relating to these changes.

### Methods of sampling

This resource contains two activities concerned with sampling.

The first activity asks students to review and summarise the key features, advantages and disadvantages of Random, Systematic, Stratified, Quota and Cluster sampling methods.

The second activity sheet consists of a set of examples of forming stratified samples from various populations. Required formulae are given.

### Professor Risk

David Spiegelhalter's actual title is Professor of the Public Understanding of Risk at the University of Cambridge. In this Cambridge Ideas video he discusses the relative risks of eating a bacon sandwich or eating a bowl of porridge for breakfast, compares the risks associated with different types of transport and considers what risks are encountered in the workplace. He shows how statistics are used to face up to life's major risks and comes to a surprising conclusion.

### Taking Decisions, Not Risks

A Mathematics Matters case study which looks at how advances in statistics allow us to analyse risks and consequences and so make informed decisions. Risks are an unavoidable part of modern life, but mathematicians and statisticians have developed a variety of methods to help mitigate its effects. These techniques enable hospitals, banks and other organisations to make better decisions, based on evidence and facts. The resource can be used by teachers to guide their students or shared directly with students to inform them about careers using mathematics.

### Representing probabilities: medical testing

This is a problem solving lesson, intended to assess how well students are able to:

- Understand and calculate the conditional probability of an event A, given an event B
- Represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams

The problem is set in the context of a new test having been discovered for a disease. Experiments have shown that:

- If a person has the disease the test will always be positive
- If a person does not have the disease, then the probability of the test being wrong is 5%, a ‘false positive result’

A series of questions follow regarding two different sample sizes.