NSW Syllabuses

# Mathematics K–10 - Stage 5.2 - Statistics and Probability Bivariate Data Analysis

## Outcomes

#### A student:

• MA5.2-1WM

selects appropriate notations and conventions to communicate mathematical ideas and solutions

• MA5.2-3WM

constructs arguments to prove and justify results

• MA5.2-16SP

investigates relationships between two statistical variables, including their relationship over time

Related Life Skills outcomes: MALS-38SP, MALS-39SP

## Content

• recognise the difference between an independent variable and its dependent variable
• distinguish bivariate data from single variable (univariate) data
• describe the difference between bivariate data and single variable data using an appropriate example, eg bivariate data compares two variables, such as arm span and height, while single variable data examines only one variable, such as arm span (Communicating)
• investigate a matter of interest, representing the dependent numerical variable against the independent variable, time, in an appropriate graphical form
• determine and explain why line graphs are the most appropriate method of representing data collected over time (Reasoning)
• describe changes in the dependent variable over time, eg describe changes in carbon pollution over time (Communicating)
• suggest reasons for changes in the dependent variable over time with reference to relevant world or national events, eg describe the change in population of Australia over time with respect to historical events (Reasoning)
• interpret data displays representing two or more dependent numerical variables against time, eg compare the daily food intake of different countries over time
• Use scatter plots to investigate and comment on relationships between two numerical variables (ACMSP251)
• investigate a matter of interest involving two numerical variables and construct a scatter plot, with or without the use of digital technologies, to determine and comment on the relationship between them, eg height versus arm span, reaction time versus hours of sleep
• describe, informally, the strength and direction of the relationship between two variables displayed in a scatter plot, eg strong positive relationship, weak negative relationship, no association
• make predictions from a given scatter plot or other graph

#### Purpose/Relevance of Substrand

Bivariate data analysis involves the analysis of two 'variables' simultaneously. It is important in the statistics used widely in everyday situations and in fields including education, business, economics, government, etc. While most single-variable data analysis methods are used for descriptive purposes, bivariate data analysis explores relationships between variables, including through the use of scatter plots and lines of best fit, and is generally used for explanatory purposes. A researcher investigating the proportion of eligible voters who actually vote in an election might consider a single variable, such as age. If wanting to use a bivariate approach, the researcher might compare age and gender, or age and income, or age and education, etc.