Select and use appropriate statistical methods to organise, summarise, display and analyse data Develop and evaluate inferences in order to make decisions and predictions based on the data
Conceptual Framework
relationships representation, pattern in the context of Globalisation and Sustainability
Statements of Inquiry
Students will understand that effectively representing and summarising data can lead to powerful methods of modelling and predicting
Factual
What are the different ways that we can represent and analyse the relationship between two variables?
Conceptual
How can we make predictions based on data for two variables?
How reliable are these predictions?
Debatable
Should important decisions be made using ‘predictions’ which follow from mathematical analysis of data?
Description
The focus of this unit will be on applying algebra and technology to represent and analyse discrete forms of bi-variate data. Students will learn about collecting, organising and appropriately rounding bi-variate data, constructing accurate scatter diagrams to represent the data, and to then analyse patterns and make inferences based on their results. Students will learn how to construct a line of best fit, visually, analytically (mean + gradient) and with technology.
Learning Outcomes
Model real-life scenarios using scatter graphs and both by hand and using technology
Understand and apply the principle of ‘appropriate degree of accuracy’ in measurements, related calculations and predictions
Construct a line of best fit using the mean point and gradient from 2-points method
Make predictions using a line of best fit
Comment qualitatively on the reliability of predictions considering (i) context of variables (ii) interpolating or extrapolating (iii) closeness to a straight-line
Understand the concept of correlation and identify appropriate (qualitative) correlation: weak/strong, positive/negative correlation, no correlation
Analyze and describe the scatter graph using terms such as weak/strong, positive/negative correlation and recognise any anomalies
Use technology to calculate a value of Pearson's correlation coefficient, r
Understand the relationship between the strength and direction of a correlation and the values of r, \( - 1 \le r \le 1\)
Use a GDC, Autograph, (and Excel spreadsheet) to generate scatter diagrams and find the correlation coefficient, r
Show knowledge of applying the r value and interpreting what it means
Recognise that a line of best fit is useless/unreliable and misleading with data sets that exhibit weak correlation
Determine the equation of a line of best fit and understand the meaning of the slope and y-intercept in context of the given data which has exhibited moderate to strong correlation
Interpolate and extrapolate data using the line of best fit and the linear equation
Understand that interpolating gives reliable outcomes, which is not always true when extrapolating
Understand the important difference between correlation and causation, and that correlation does not imply causation
Apply the skills learned to larger sets of real-life or secondary data that may or may not have linear correlation with or without causation