Data : Data involving one and two variables

Data types

• Qualitative data involves non-numerical variables that can be organized into categories, such as types of sports, modes of transportation, or colours. Also called categorical data.
• Quantitative data involves numerical variables obtained by counting or measuring and expressed as a number or quantity. There are two types of quantitative variables: discrete and continuous.
  • Discrete quantative variables
    • have a finite value. They can be counted.
    • can only take on certain values from an interval of real numbers, usually integers (for example, the number of faces of a three-dimensional object, the number of people in a family).
    • can also take on values that are not integers (for example, shoe size can be \(7\) or \(7\frac{1}{2}\).).
  • Continuous quantitative variables
    • can be mesured.
    • can take all possible values from an interval of real numbers (for example, the mass of a dog, the volume of a cone).

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Data analysis

• For a sample to be representative of a population, it must be collected:
  • Appropriately: the method of selecting the sample must be well thought out to ensure that each group in the population has an equal or proportional chance of being included, avoiding bias.
  • Systematically: the data collection process must follow a systematic and consistent procedure to ensure that the sample accurately reflects the diversity and characteristics of the entire population.
• Analyzing measures of central tendency and the distribution of a dataset (mean, median, mode, range) is essential for drawing relevant conclusions. For example, the mean is a good indicator when the data range is small, but not a good indicator if there are a number of outliers.
• The choice of graph or diagram used to visualize the data should be based on the nature of the data (quantitative or qualitative) and what one aims to demonstrate, analyze, or communicate with it.
• Regression models are statistical tools used to determine the correlation between two variables. They help determine if and how the dependent variable is affected by the independent variable. This relationship can be represented by linear models (for example, a straight line) or non-linear models (for example, polynomial, exponential, logarithmic).

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Mathematical Modelling Process

• The mathematical modelling process involves:
  • formulating questions and making assumptions;
  • determining the relevant data to collect based on the question analyzed;
  • developing and implementing an appropriate data collection plan;
  • creating a mathematical model adapted to the data and answering the question;
  • analyzing, evaluating and modifying this model.

Modelling. The diagram is made up of 4 boxes, some of which are linked together by double arrows. Boxes 1, 2 and 4 are superimposed on a grey circle. Above boxes 1 and 2, it says: “Real-Life Situation”. Box 1 is entitled “Understand the problem”. It reads as follows. First bullet point: “What questions need answering?” Second bullet point: "What information in needed?” It is linked it to box 2, which is entitled “Analyse the Situation”. Box 2 reads as follows. First bullet point: “What assumptions do I make about the situation?” Second bullet point: “What changes, remains the same?” It is linked to box 3, which is entitled “Create a Mathematical Model”. Box 3 reads as follows. First bullet point: “What representations, tools, technologies and strategies will help build the model?” Second bullet point: “What maths concepts and skills might be involved?” It is linked to box 4, which is placed under boxes 1 and 2, to which box 4 is also linked. Box 4 is entitled “Analyse and Asses the Model”. Above box 4, it says: “Share and Act Upon Model(s)”. Box 4 reads as follows. First bullet point: “Can this model provide a solution to the problem?” Second bullet point: “What are the alternative models?”

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Data types, Diagrams and Graphs

The table below provides an overview of the types of data and diagrams students will be working with at each grade. Note that diagrams from previous years are still relevant in the current year, depending on the type of data being analyzed.